Morahan, who has the ability to play on the wing, at full-back or at centre has expressed his excitement over the move.
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“I’m excited about the opportunity to play in England, but also to be a part of the ambitious journey that Bristol Rugby is on,” Morahan told Bristol’s club website.
“I am confident that everything is in place at Bristol for us to be a successful club.”
The versatile Morahan will leave the Force after three seasons with the club.
Bristol interim head coach Mark Tainton was impressed by Morahan and looks forward to the Australian joining the struggling side.
“Luke is an impressive player with excellent technical abilities and a lot of raw pace,” Tainton said.
“We were really encouraged by Luke’s attitude and enthusiasm throughout the recruitment process.”