The 27-year-old joined Rhinos on loan from Warrington Wolves in July and made seven appearances in Leeds’ successful battle against relegation.
His Warrington contract expired at the end of the season and he has now signed for Rhinos on a permanent basis.
Crosby made it clear from the start he was keen to earn a long-term deal and said: “I’m delighted to have signed with Leeds Rhinos for the next three years and extremely excited and grateful for this opportunity.”
He added: “It is a club with a great history and passionate fans and I’m proud to be a part of it.
“I can’t wait for pre-season and I look forward to giving my best for the club and my team mates.”
Crosby played 102 games for his hometown club Wigan from 2012-2016, featuring in four successive Grand Finals and collecting two winner’s rings.
A former Hindley junior, he also had spells on dual-registration with Widnes Vikings, South Wales Scorpions and Leigh Centurions.
He joined Warrington in 2017, making seven appearances that year and another 10 in the following campaign.
He made his Rhinos debut in a Betfred Super League win over Widnes Vikings, but was suspended for two games following separate incidents in the opening Qualifiers clash with Toulouse Olympique, when he made his first start.
He returned for the final four games of the campaign and his new deal was agreed following director of rugby Kevin Sinfield’s end-of-season review.
Sinfield said: “We are pleased to have secured Dom for the next three years.
“He impressed everyone at the club with his attitude on and off the pitch and I am sure he will make big strides after a full pre-season with Leeds Rhinos.”
Of what Crosby brings to the squad, Sinfield added: “As we look towards a new era for the team it was important we secured players of Dom’s experience, having been a winner during his time at Wigan and I am sure he will have a big influence on the group, especially our young forwards.
“At 27 he is coming into his prime as a prop and he will benefit from working with [new coach] Dave Furner during the closed-season.”
Crosby’s permanent deal comes two days after Rhinos confirmed former Wakefield Trinity and Hull FC boss Richard Agar’s appointment as head of player and coach development.
“He is purely about developing our next players and our next coaches, he has no first team involvement,” Sinfield said of Agar.
“He will have no day-to-day involvement with the Rhinos first team, he’ll be working with everybody from the under-19s down in the male game.
“It is the same role he has been doing at St George-Illawarra and his reputation overseas speaks for itself.”