BOSTON -- Doug Fister’s short time with the Red Sox brought revised mechanics, improved velocity and enough success to warrant legitimate interest elsewhere.

The right-hander has agreed to a major-league deal with the Rangers, pending a physical, a person with knowledge of the agreement told NBC Sports Boston.

Fister, entering his age-34 season, had a 4.88 ERA in 15 starts and three relief appearances for the Sox during the regular season. What’s not reflected in the ERA are increases in both his velocity and strikeout numbers. He fanned 8.3 per nine innings, up from an average of 5.6 per nine innings in the three seasons prior.

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The Sox are pursuing power hitting and lefty relief help, but apparently feel content with their collection of potential rotation rams.

“I don’t think that’s a main priority for us this winter time, starting pitcher,” Sox president of baseball operations Dave Dombrowski said in mid-November. “Because I think we like our starting pitching. However, as the winter progresses, if somebody’s out there that makes sense to add, I wouldn’t say that we definitely would not do it, but I’m comfortable where we are.”

Fister had a poor showing in his Game 3 start in the Division Series, lasting 1 1/3 innings. Nonetheless, the Sox coaching staff was a significant help to Fister, allowing for at least the possibility someone else now will benefit from the hard work they put in to assist Fister’s own diligence. Among the suggestions was a move to the first-base side of the rubber, helping to alleviate some physical stress in his delivery. That idea came from recently promoted pitching coach Dana LeVangie.

“Working on the sinker depth, working on getting the curve ball spin right and then you know kind of just reacting to how the league is this year,” assistant pitching coach Brian Bannister said during the year. “It’s been harder on sinker ballers in general, just because guys are going all or nothing with their approach. So he has been working on different strategies to kind of evolve himself in how he mixes and how he attacks the zone, and now kind of the final thing is working on getting some depth on the changeup like he had in years past.

“It’s been impressive to watch him work, to watch him try and pitch competitively while also making all these adjustments, because he went in a very different direction last year in Houston. And unwinding that, while also trying to get back to some of his strengths -- while also trying to add something new -- it’s been fun to watch him, and it’s really good to see him have success. Because he’s a pitcher who was extremely successful at one point, who is still very talented, has an athleticism and a range of motion you don’t usually see in a 6-foot-8 guy. And so there’s a lot of talent there, a lot of things to work with, and he’s put in the time.”

Fister didn’t make his first major-league start of the year until June, when the Sox claimed him off waivers from the Angels, who had him at Triple-A. Fister proved a worthwhile, low-risk pick-up, and in many ways that remains his profile as a free-agent signee.

“I’m very -- I don’t want to say content, but if my career stopped right now at this point, today, you know I can hang my hat on knowing I've done everything I could to have a successful career,” Fister said in August when asked if he worried his career could be over prior to joining the Sox. “Maybe there’s some people out there that wanted to, needed to see it or I needed to prove it to somebody. But I have always felt that I still had what it takes to be a starter and I still feel that. You know, I’ll feel that ’til the day I hang up my cleats. Even if I’m in the bullpen. Either way, it’s fine. I’ve got have it in my heart that I know I can go out and get a big league hitter out at any point.”

Fister had a 2.79 ERA in a seven-start stretch from July 31 to Sept. 6, holding opponents to a .194 average in that time.