Tim Healey of Newsday also confirmed the news.
The new manager will receive two guaranteed years on his new contract to go with team options, per Jon Heyman of MLB Network.
Rojas was the team's quality control coach, a role he assumed in December 2018. The 38-year-old interviewed for the managerial job this past fall when the Mets were replacing Mickey Callaway but lost out to Beltran.
His father is three-time All-Star and former manager Felipe Alou, and his brother is six-time All-Star Moises Alou.
SNY's Andy Martino reported Rojas was one of three finalists for the job alongside Hensley Meulens and Tony DeFrancesco. Martino added that the Mets saw the "benefits of going internal."
Per Joel Sherman of the New York Post, the rest of the coaching staff will stay intact.
Beltran lasted a little over two months with the Mets before he and the team mutually agreed to part ways amid the fallout from the Houston Astros' sign-stealing scandal.
General manager Brodie Van Wagenen addressed the breakup in a statement:
"Here's the best way I think we can describe it: When we met with Carlos, we had to make an assessment of, 'Where do we go from here?' In Carlos' thought process, as well as ours, we both agreed that it was going to be incredibly challenging, and incredibly difficult to do the job in the way in which he intended, and the way in which he can utilize the best of his abilities."
Following an investigation, MLB determined the Astros used a system to electronically steal signs from opposing teams throughout the 2017 season. Beltran was the only player named in the league's final report among those who were involved in the strategy.
Although the 42-year-old avoided a suspension, many wondered whether his position had become untenable.
The Astros fired manager AJ Hinch and general manager Jeff Luhnow, while the Boston Red Sox moved on from manager Alex Cora for their roles in the scandal.
Especially after those moves, the Mets had little choice but to jettison Beltran. By doing so, of course, they inevitably disrupted their offseason.
One thing that separates New York from Houston and Boston is that the team didn't truly know what it had with Beltran in the dugout.
The Astros and Red Sox lost managers who guided them to World Series wins. Beltran was well-regarded by his teammates and looked like a manager-in-the-making toward the end of his playing career. But nobody can say for sure how he would've done in the Big Apple.
Because of that, his departure may not significantly change the Mets' outlook for 2020.
At best, they might be the third-best team in the National League East behind the reigning champion Washington Nationals and Atlanta Braves. The Philadelphia Phillies could overtake them as well after signing Didi Gregorius and Zack Wheeler.
New York, meanwhile, has only made incremental moves (acquiring Jake Marisnick and signing Rick Porcello, Dellin Betances and Michael Wacha).
Even with Wheeler's departure, the Mets still have one of the best starting rotations in baseball, yet Mets fans know all too well how risky it can be to count on your starters staying healthy.
As much as Beltran's presence could've provided some optimism for the future, he may have been limited in the short term based on the obvious holes in New York's lineup.
Now, Rojas will be taking charge. The question is whether he'll be the long-term answer or if the Mets intend to keep their options open and find a more permanent solution next winter.