"Billy's a great player, and he's shown for Leicester that he can play right up there and produce the goods against the best teams," Burns told This is Gloucestershire.
"He's a great guy for the club to be able to bring in, a great signing, and I'm just looking forward to playing with him. He's able to play to a high level in a variety of styles, and I think that's exactly what we need.
"Things went well at the Saxons when we played together and hopefully we can rebuild that at Gloucester. We have a similar kind of approach to the game, and I'm confident we can strike up a good partnership quickly."
Twelvetrees is capable of playing in the centre or at fly-half.