The first of the two programmes, There's Only One Michael Mosley, will air on BBC Radio 4 and BBC Sounds at 11:00 BST on Friday 14 June.
It will feature the last interview Dr Mosley conducted, recorded in the BBC tent as part of the Hay Festival in May.
For the interview, titled How to Live a Good Life, Dr Mosley spoke to Paul Bloom, Professor Emeritus of Psychology and Cognitive Science at Yale University.
The BBC says it sees the presenter "at his best, full of warmth, insight and thoroughly enjoying his time with the audience".
A second special programme, Michael Mosley - The Doctor Who Changed Britain, will air on BBC One and iPlayer on Friday 14 June at 20:00 BST.
The programme will "look back at an extraordinary broadcasting career which spanned almost 40 years", the BBC says.