The Celtics will send the Thunder a conditional second-round pick. Boston gets the 2019 second-rounder Oklahoma City had acquired from the Detroit Pistons.
The trade is strictly a luxury-tax move for the Thunder, who after recently signing Enes Kanter to a $70 million deal will save roughly $7 million by trading Jones.
The deal also will create a $2.1 million trade exception for the Thunder.
Jones averaged 4.3 points and 1.8 rebounds in 43 games last season with the Thunder. He flashed his potential, though, during a three-game span early in the season when he filled in for the injured Kevin Durant and scored 32, 20 and 16 points, respectively, before badly bruising his knee and missing the next 13 games.
With a young roster in Boston, the 23-year-old Jones will fit nicely into the Celtics' plans. He's a 6-foot-11 athletic specimen, a player Durant once called "the best athlete in the league."
"Oklahoma City has a great deal of depth on their frontcourt, and so we've watched [Jones] play and followed him in his college career. He's a terrific athlete," Celtics president of basketball operations Danny Ainge said. "His game is much different than a lot of the guys that we have under contract right now. We'll see how he fits in with our system."
Ainge said the team considered picking Jones during the 2012 draft (the year Boston landed Jared Sullinger at No. 21, then misfired a pick later with Fab Melo).
The Thunder selected Jones out of Baylor 28th overall after he surprisingly slipped to the bottom of the first round.
The Celtics were able to use available cap space to acquire Jones and a future pick at virtually no cost to the team.
"The benefit [to cap space] is getting assets, sorta like we did last year [by acquiring] Tyler Zeller and Cleveland's first just by having the trade exceptions," Ainge said. "This is a similar situation to that."
The Thunder can lower their luxury-tax number even more by offloading forward Steve Novak (making $3.75 million), a move they might look to make, although a deal in that regard isn't imminent.
ESPNBoston.com's Chris Forsberg and The Associated Press contributed to this report.