There was no such negotiations with binding promises made public aside from interwebs rumors, frequently reposted on RT/Sputnik/etc. The end of Cold War was USSR unilaterally dissolving by agreement between Russia, Belarus and Ukraine.
Furthermore, Yeltsin publicly said that eastern europe can join NATO if they wish. The only request was that there would be no nuclear weapon moved to new NATO members. And there were talks about limiting conventional weapons. That's why current NATO forces in Baltic states and Poland are "rotational" rather than permanent.
https://www.nytimes.com/1997/04/18/world/yeltsin-now-seems-r...
> In the 90s the Russian were sticking mad as hell about this stuff, they just didn't have the power to do anything about it. In the last 15 years the have learn that they can, so they do.
As an ex-USSR citizen, Russia was damn friendly in early 90s. Russian SSR (separate from USSR) supported Baltic states during January events of 1991. Russian army was rather swiftly removed. Separation was rather smooth thanks to mutual understanding. Things started to change in late 90s though. Not sure where the braking point was.