Brown, who has made three England 'A' appearances, will join up with his new team-mates at the beginning of next season.
The second rower, who will be 24 on Saturday, joined Bristol straight from Colston's School, and was a key element in the Bristol side that won the inaugural Under-21 Zurich Premiership.
"Coming to Gloucester is a step up and one I am very excited about," said Brown.
"I have played at Kingsholm before and I have to say that I would rather have the support on my side rather than against me," he added.
Brown was part of the Bristol side that qualified for a Heineken Cup place this season and is looking forward to playing against the best in Europe next season with the 'Cherry and Whites', who have already qualified for Europe's Premier Club competition.
"I really enjoyed the experience of playing in the Heineken Cup this year, it is a step up from the Premiership, and I can't wait to play in that level of competition again next season."
He has played under Dean Ryan whilst the Gloucester coach was at the Memorial Ground and described him as 'awesome' adding, "I am looking forward to renewing our partnership next season."
"I am delighted that Alex has decided to join Gloucester," said Nigel Melville, Gloucester's Director of Rugby. "He is another of the young up and coming English players and I am looking forward to seeing what he can do for us next season."
