Machado's deal is for $16 million, while Britton will earn $12 million, according to multiple reports. Both players will be free agents at the end of the 2018 season.
Britton is likely to miss several months of the regular season after rupturing his Achilles tendon in December. The initial timeline for his return was set at six months.
Reports earlier Friday had the O's heading to an arbitration hearing with Machado after failing to agree by the 1 p.m. ET deadline. However, the two sides were able to find common ground. Machado made $11.5 million in 2017.
The 25-year-old Machado, whom the Orioles are considering moving back to shortstop next season, hit .259 with 33 home runs and 95 RBIs in 2017. The three-time All-Star began the year in a lengthy slump (.230 batting average in first half) before hitting .290 down the stretch to salvage his season.
Britton, 29, was limited to 38 games while battling an MCL sprain in his left knee and had a 2.89 ERA and 15 saves. The left-hander was the best reliever in baseball in 2016, posting a 0.54 ERA and going 47-for-47 in save chances on his way to finishing fourth in the American League Cy Young vote.
Britton earned $11.4 million in 2017.
Both Machado and Britton have been the subject of trade rumors this offseason, with talks surrounding the latter quieting down following his injury.
Baltimore also agreed to terms on a one-year deal with right-handed reliever Brad Brach worth $5.165 million, according to a report from MASN Sports. Brach, 31, had a 3.18 ERA while picking up in 18 saves in place of Britton last season.
Shortstop Tim Beckham agreed to a $3.35 million deal for 2018, according to a report from The Baltimore Sun. The 27-year-old former No. 1 draft pick hit .306 with 10 home runs and 26 RBIs in 50 games with the O's after being acquired from the Tampa Bay Rays ahead of last year's trade deadline.
Catcher Caleb Joseph agreed for $1.25 million, according to a report from BaltimoreBaseball.com. Joseph, 31, hit .256 with eight home runs and 28 RBIs in 2017.
Other arbitration-eligible Orioles players include second baseman Jonathan Schoop and right-hander Kevin Gausman.
--Field Level Media