Trevor Rabin was in a couple of bands, then released a few solo albums, before teaming up with Chris Squire and Alan White, which eventually became a reformation of Yes. 90125 launched Rabin to stardom.
I heard the singer from Tin Machine had a prior solo career. Some of his stuff is pretty good.
The one I could think of is almost certainly an edge case, in that I wouldn’t consider them a ‘very famous band’ and that the solo career was one of many ups and downs. Anyway, my nomination is for Kris Kristofferson and his work as part of the Highwaymen. For me it qualified in that I found the artist as part of the supergroup and then backtracked his individual work. But again, a very edge case. And now I most go listen to the song in question again because I love it and it’s stuck in my brain!
Brian Johnson doesn’t quite qualify per the OP, as he was in the moderately successful band Geordie before going solo. He later found immense fame as Bon Scott’s replacement in AC/DC, recording the second-best selling album of all time.
I suppose Adam Lambert might qualify.
As a fan of Yes, I was thinking of posting about Rabin last night, but when I did some reading, I discovered that his most notable earlier band, Rabbitt, was in existence for six years, had several albums, and a #1 hit in their native South Africa (though I think that they had little or no airplay in the U.S.). So, at least in my mind, he didn’t qualify for the OP. 
Ronnie James Dio had had a solo career and fronted a couple of bands before he joined Black Sabbath.
Technically, Patty Smyth was Eddie Van Halen’s first choice, but your point is still valid.
I’d say David/Davy Jones is pretty much the model of what I was looking for. He definitely released a solo album and had a Hot 100 single, but he clearly went on to new heights with the Monkees and he’s certainly much better known as a member of them than for anything he may have done as a solo artist after the Monkees’ run ended.
I just read on Wikipedia that he was on the same episode of the Ed Sullivan show as the Beatles, promoting the stage show he was acting in, and seeing the girls go crazy for the Fab 4 wanted to become more like them and that caused him to change from acting to singing.
Some others mentioned might work as well, but I’d not ever heard of them, while I definitely heard of Davy Jones.
And whenever I talk about Davy Jones, I’m always reminded of Kingdom of Loathing doing a gag where you find Mike Nesmith’s locker.
Here’s a surprising one:
Narada Michael Walden has produced records for Aretha Franklin, Stevie Wonder, and Mariah Carey, among many others. He’s won three Grammys.
He’s also been a prolific solo artist, releasing 10 major-label solo albums, mostly in the late Seventies and early Eighties. His singles have reached the R&B and dance charts.
Last year, at the age of 68, Walden was hired as the drummer for Journey.
(?!)
If this is open to rap duos and groups, then I would say Run The Jewels (2013- present) is the most successful project for El-P (Company Flow mid-90s, then solo til 2013) and Killer Mike (Outkast associate, Grammy and 1 semi “hit” Album in early '00s but completely underground as a solo artist since), who’ve had 25+ and 20+ year careers as solo artists and in previous groups and collectives. Went from playing small bars and respectable underground sales figures to selling out tours in pretty large venues, the large font top billing for festivals, Gold singles, really big crossover merch and media placements, top 10 billboard albums with multiple sold out deluxe editions despite every official album being available for free, and so on. Two rappers in their mid-40s.
Speaking of which…I’ll stretch a bit and suggest Steve Perry: In and out of bands that didn’t get signed (Ice, Pieces, Alien Project), Steve had given up and gone back to the family farm when Herbie Herbert reached out to him after hearing a demo tape from Alien Project.
[Neal Schon, who had been invited to join Eric Clapton’s band one night, and then was invited the next morning to join Carlos Santana’s band, was soon urged to get out of Santana’s shadow and form his own group. He pulled Gregg Rolie with him and found a couple others to create a progressive/jazz-influenced instrumental group, and found a guy named Fleishman to do lead vocals – but they didn’t all get along great with Fleischman – and played the San Franciso Bay area.]
Perry joined a tour as the cousin of one of the roadies, then performed a couple songs with Journey during a sound-check. Herbert announced they had found Fleischman’s replacement. [I wonder how he took that when he came back from his bathroom break.]
The rest, as they say, is history.
–G!
I think Major Lazer is more successful than solo Diplo
Completely opposite is Gram Parsons who was in the Byrds and Flying Burrito Bros before going solo. He released two beautiful, brilliant solo albums before OD’ing about one month short of joining the 27 club.
Parsons also had released “Safe At Home” with the International Submarine Band before joining the Byrds, which is considered the first country rock album by many. It’s a very fine album.
Not exactly a solo career, but prior to joining the Grateful Dead, Donna Jean Godchaux was a studio backup vocalist in the 60s and performed on many hits including “When A Man Loves A Woman” and “Suspicious Minds”.
Tammi Terrell had a short stint as a solo act with Checker records, then signed with Motown, never got a solo recording higher than #72. Then she was teamed up with Marvin Gaye and the duo had 5 Top 10 records.