Stagecoach said the route over the Forth Road Bridge would launch on 15 May.
The 14-mile route will run between Ferrytoll park and ride in Fife and Edinburgh Park train and tram interchange.
Five single-decker autonomous buses will have the capacity for about 10,000 passenger journeys per week.
The vehicles have sensors enabling them to travel on pre-selected roads at up to 50mph.
They will have two members of staff on board.
A safety driver will sit in the driver's seat to monitor the technology, and a so-called bus captain will help passengers with boarding, buying tickets and queries.
The UK government said Project CAVForth would be the world's first full-size, self-driving public bus service.
Scottish government Transport Minister Kevin Stewart said: "This is an exciting milestone for this innovative and ambitious project, and I very much look forward to seeing Project CAVForth take to the roads next month.
"Our trunk road network can provide a wide range of environments as a diverse testing ground, and the ground-breaking and globally significant project will really help Scotland establish its credentials on the world stage."
Stagecoach UK managing director Carla Stockton-Jones added: "We are excited to introduce the UK's first autonomous bus fleet in east Scotland which is also home to our headquarters and where it all began over 40 years ago.
"We are proud to be at the forefront of transport innovation with this project that marks a significant milestone for public transport and we look forward to welcoming our customers on board in the coming months.