The 23-year-old flanker has won six caps, and scored 16 tries for the Bees this season.
Gloucester head coach Dean Ryan said: "In Akapusi, I think we have unearthed someone who can have a real impact on the Premiership.
"The English first division is a tough league for someone to come over and make a name for themselves, but he has played nearly every game for the Bees and his try-scoring ratio for a forward is exceptional.
"As you would expect from someone who is 6ft 4in and weighs in at over 100 kilos, he offers a big physical presence around the park, but even allowing for his size, his athleticism and strength in contact is something else.
"Hopefully, he can continue his good form through the summer and play a key role for Fiji at the World Cup."