Well-researched, largely historically accurate fiction:
Wolf Hall and Bring Up the Bodies by Hilary Mantel. It’s about Thomas Cromwell as he rises to become one of Henry VIII’s most trusted advisors.
The Killer Angels by Michael Shaara. The Battle of Gettysburg, seen through the perspectives of Col. Joshua Lawrence Chamberlain on the Union side, and Gen. James Longstreet on the Confederate side.
Nonfiction that moves almost like fiction: The Guns of August by Barbara Tuchman.
Sarum by Edward Rutherford. It’s the history of London from Roman times up to the 19th century. It reads like fiction because there are several fictional families interwoven in the story.
I can’t recall his other titles right now but he’s written a few books about particular places using a similar formula. His research always shocks and delights me.
“An Insular Possession” by Timothy Mo is a fictionalised account of the establishment of Hong Kong. It’s very good.
The Princes of Ireland and The Rebels of Ireland are about, well, the history of Ireland. IIRC, they start in the 400s and end sometime following WWII, but I could have the timeline extended or shortened. Great reads, and relatively historically-accurate, ignoring the fictional families.
From his Wikipedia page, he’s written books about London (Sarum and London), as well as ones about New York, Russia, Paris, and the New Forest in Southern England.
Came in to mention Tuchman’s A Distant Mirror, which has been recommended a few times already. Tuchman’s genius was to structure the whole book, which is a history of Europe in the 14th century, around the life of Enguerrand de Coucy, a French nobleman who lived through it’s latter half. Coucy was well-connected - he became the son-in-law of King Edward III of England - and managed to be involved in most of the important events of the century, and Tuchman uses him to put a human face on what could have been a dry chronicle of wars, plagues, and invasions.
Another option for well-researched historical fiction are Patrick O’Brian’s Aubrey/Maturin novels, a 20-book series about a Napoleonic War English naval captain and his close friend, a physician and intelligence agent.
Charles Macdonald Fraser is another novelist who did his homework. His Flashman series is immensely entertaining, due to his cheerfully amoral scoundrel of a protagonist. And some of his stories sound like the wild imaginings of a mystery novelist. Yet they are meticulously researched and, save for the fictional Harry Flashman and some of his friends, true.
Although not written in a fictional style The Story Of Mankind By Hendrick Van Loon is very readable.
“The Last Battle” by Stephen Harding: American and German soldiers team up to prevent German SS troops from capturing and killing important French politicians, generals and civilians in the closing days of World War II. Sounds like a pitch for a bad movie like “The Dirty Dozen”. Immediately after the battle is won the French started writing memoirs to vindicate themselves and blame the others. Now that is believable.
I’d recommend “Death in the City of Loght” about a manhunt for a serial killer in occupied Paris during WWII.
I came to recommend both of these. They’re fascinating.
One of my favorites,that I think meets the OP’s request is Gates of Fire, a historical fiction version of the Battle of Thermopylae (much more fictionalized in the movie 300)
Err, that’s Death in the City of Light. Phone posting can cause spelling problems.
And i like the fact that the OP asked for non fiction books and so many people are giving them novels.
I opened this thread to recommend that one.
If you want actual history of a very high quality by the same author, you have some choice: he wrote what is widely considered one of the best personal memoirs to come out of WW2 by a fighting man: Quartered Safe Out Here. He also wrote a book that falls squarely within the OP’s requirements - a work of stranger than fiction history, pre-1800s - a history of the anglo-scottish border reivers entitled The Steel Bonnets.
I highly recommend both.
The latter, in particular, is on what appears to be an obscure topic (clans of raiders and vicious criminals who lived in the “debatable” border regions from the 13th through the 16th centuries). However, these clans made a big impact - in America. Which is obvious when you see the clan names - the author points out that, at the inauguration ceremony of President Richard Nixon, he was flanked by Lyndon Johnson and Reverend Billy Graham - all three last names were major Clan names from the Debatable Land.
The Debatable Land itself sounds exactly like a post apocalyptic wasteland, Mad Max-style (only, Elizabethan). In this area, normal laws were suspended and the clans ruled supreme - with robbery, pillaging, and murder. The authorities positively encouraged this bizarre state of affairs for reasons of their own …
Another suggestion is a book I’m reading right now, that just came out in 2016: Jungle of Stone, by William Carlsen. It’s a history of the two men who popularized in Europe and America the ancient Maya ruins (they did not discover them - but they provided the first accurate account of them to a non-local audience).
Their story is truly stranger than fiction: one of the men was in the area as a US diplomat, attempting to get a trade treaty signed – during a revolution (after many hair-raising escapes from death, including interviewing the generals on both sides, he gives it up, writing to Washington: “after diligent search, no government found”). All along, though, his real mission was to hunt down rumors of massive stone ruins in the jungle - and in that quest, he succeeded beyond his wildest dreams.
Fortunately he had his friend along, an artist who could make extremely accurate drawings of the ruins - the first accurate glimpse outsiders were able to get (there had been previous drawings, but they were either held secret by governments, made by non-artists, or in some cases, deliberately falsified to make the ruins look like Roman or Egyptian ruins!).
The pair go through incredible hardships and dangers, and have many bizarre encounters along the way - a sort of cross between Indiana Jones and Innocents Abroad. 
Thank you so much for this recommendation. I loved this book!
Am I the first to mention Tom Wolfe’s excellent The Electric Kool-Aid Acid Test?
Since The Devil in the White City has been mentioned so often, I’ll simply concur with it’s excellence.
I’d add Longitude: The True Story of a Lone Genius Who Solved the Greatest Scientific Problem of His Time, about the 18th century man who was able to solve the problem of determining longitude on long voyages. It sounds like the driest topic on earth, but the author somehow makes it exciting and page-turning.
It is awesome - and they made a TV mini-series based on it! 
Which is, likewise, awesome.
I’ve read two of the suggestions:
Really enjoyed The Sea Captain’s Wife and liked how the author interleaved different contemporaries perspectives into the narrative.
I have to admit … I got half way through A Distant Mirror before I got sick of who was fighting who! I recognise that a lot of the records from that period of time will be about battles etc but I found the lack of “character” and “real” life people (not kings/knights etc!) fairly uninteresting. I rarely give up on a book … so might go back to it another time.
Next added to my kindle with thanks for everyone’s suggestions:
Unfortunately not available on kindle but I thought this sounded interesting:
I’ll return to this book list as I enjoy my holidays!