The Crabbe offer sheet was first reported by The Vertical and confirmed by ESPN.
The contract could reach up to $83 million in bonuses and includes a player option for the fourth season, sources told ESPN.
The Trail Blazers have three days to match the offer.
This is the second restricted free-agent offer sheet Brooklyn general manager Sean Marks has given out. Miami Heat restricted-free-agent guard Tyler Johnson signed a four-year, $50 million offer sheet with Brooklyn, which contains a poison-pill provision.
Marks has been aggressive in rebuilding the Nets, also signing Jeremy Lin (three years, $36 million) and agreeing with Trevor Booker (two years, $18 million) and Justin Hamilton (two years, $6 million).
Crabbe, 24, emerged as a quality scoring threat off Portland's bench last season, when he averaged 10.3 points in 26 minutes per game and shot 45.9 percent from the floor and 39.4 percent from 3-point range.
The 31st overall pick in the 2013 draft, Crabbe seized an opportunity for a significantly increased role in 2015-16 due to the Trail Blazers' youth movement. He played in only 15 games as a rookie and averaged only 3.3 points in 13.4 minutes per game in his second season.
Information from ESPN.com's Tim MacMahon was used in this report.
Windhorst amazed by Nets' offer to Allen Crabbe
Brian Windhorst calls the Nets' offer sheet to Trail Blazers restricted free agent Allen Crabbe "breathtaking" and questions if Portland will match the offer.