No they are more than “gentlemen’s agreements” and they are enforceable. Exactly how they are enforced will vary.
From the Wikipedia article on plea bargaining:
Santobello v. New York added that when plea bargains are broken, remedies exist; and it has been argued that given the prevalence of plea agreements, the most important rights of the accused may be found in the law of contracts rather than the law of trial procedure.[9]