The Brooklyn Nets have signed restricted free-agent forward Donatas Motiejunas, as expected, to a four-year offer sheet potentially worth as much as $37 million, according to league sources.

But sources told ESPN.com on Friday night that the uniquely structured deal is fully guaranteed for only $5 million of that total and rising to $17.5 million if Motiejunas has earned his 2017-18 option by March 1, terms that could well encourage the Houston Rockets to match the Brooklyn offer sheet.

The Rockets will have a 72-hour window, ending at Monday at 11:59 p.m., to decide whether to match the offer or let Motiejunas join the Nets.

"I have to talk to the owner before we make a decision," Houston general manager Daryl Morey said Friday night. "There's been a lot of restricted free agents that went late into the season, several into December. It's a process that's part of how things work. Sometimes it takes a little longer, but we're happy it's going to come to a resolution."

The Nets have been weighing the move internally for some time and, according to sources, are "comfortable" with where Motiejunas is medically, after back issues scuttled the Rockets' trade of ‎him to the Detroit Pistons in February.

That history of back trouble, however, led the Nets to structure Motiejunas' contract with a number of protections against long-term risk. Sources say he will earn $5 million immediately just by signing the contract, but the team that has him on its roster as of Tuesday must decide by Jan. 10 whether to guarantee an additional $3.5 million for this season or let him go at that point. By March 1, sources said, Motiejunas' full $9 million option for the 2017-18 must then be picked up or declined.

"I'm happy," Motiejunas, a 26-year-old native of Lithuania, told ESPN's Calvin Watkins on Friday. "It's [been] way too long, I waited so long; I just wanted to play basketball.

"Even better, it showed they believed in me," Motiejunas said of the Nets. "They put me through a number of tests [on his back], and they saw that I'm as healthy as anybody else. After Detroit, everybody was questioning me. They showed a commitment that I'm going to be a piece of their future; if not, I'll be happy with Houston, too."

After signing the offer sheet, Motiejunas flew to Houston, where he will await the Rockets' decision on whether to match it. Although the final two seasons of the contract are non-guaranteed, Motiejunas ‎can clinch the total of nearly $18 million in guaranteed money if he plays into March with no health issues.

‎Houston pulled its most recent offer to Motiejunas on Nov. 22, when the sides couldn't come to terms on a deal before the Rockets' self-imposed Nov. 22 deadline.

‎Nov. 23 was the last day that players could be signed this season and remain eligible to be dealt on the league's annual trade-deadline day, which falls on Feb. 23. ESPN reported in early November that the Rockets, as a result, picked that date as their own internal deadline to sign Motiejunas, fearing his value would decrease if they didn't have the ability to trade him.

The Nets, sources said, specifically waited until this week to sign Motiejunas, in part because they hope Houston will be less inclined to match an offer for him now. The Rockets will be unable to trade Motiejunas for a year without his consent if they elect to match the offer.

The Nets had more than $18 million in available salary-cap ‎space to assemble an offer Houston might find unpalatable. New Nets general manager Sean Marks, though, was foiled twice in restricted free agency over the summer, seeing hefty offer sheets to Miami's Tyler Johnson (four years, $50 million) and Portland's Allen Crabbe (four years, $75 million) matched by those teams.

Sources told Stein on Nov. 4 that the Rockets were offering a two-year deal starting in the $7 million range but with only the first season fully guaranteed for the 7-foot, 223-pound Motiejunas.

ESPN reported last week that Motiejunas was "surprised and upset" that negotiations with the Rockets had dragged on so long. Motiejunas could have made himself an unrestricted free agent next summer had he been willing to play out this season on Houston's $4.4 million qualifying offer, but he let the qualifier expire Oct. 1, hopeful that a long-term deal would materialize.

The Rockets have been unwilling to guarantee more than the first year of a multiyear deal in a nod to Motiejunas' injury history. Houston traded him to Detroit in February, only for the Pistons to void the deal and send him back to the Rockets because of a failed physical stemming from Motiejunas' back troubles.

ESPN's Calvin Watkins contributed to this report.