1133 BMP-1 were taken over from the NVA. 764 of these were planned for conversion for the Bundeswehr, 19 were sold to the USA, 350 were sold to Sweden (this is also the number Jane's lists).
Bundeswehr conversion stopped at 586 units though, and the leftover units were sold again. 140 of these units went to Finland and up to 28 went to Sweden, for a total of about ~375 - the number you usually see on the Internet.
SIPRI lists 366 BMP-1 plus 66 spares (which might have come from Poland though) delivered. There were spare parts in NVA depots, and while these might have made up 66 BMP-1 altogether, i doubt these were delivered assembled.
Of the 24 BMP-2 taken over from the NVA two were sold to France and 15 to the USA. No idea where the remaining 7 went to.
With MT-LB it's far more complex, as the Bundeswehr didn't consider these combat vehicles and therefore didn't publish the numbers taken over. One combination i've seen lists 766 MT-LB of all types used by the NVA, which probably comes closest to the number 800 you generally read on the Internet.
SIPRI lists 622 MT-LB(u) plus 215 spares plus 228 2S1 chassis delivered. There are other sources claiming e.g. either 550 or 700 delivered, so there's a lot of ambiguity.