General manager Jon Daniels, making the announcement after Friday's game, said the Rangers will try to trade Feliz.
"It was a tough call," Daniels said. "Mostly from the fact that Neftali has been on most of the great moments in franchise history. He is still young, talented and works hard. But the consistency wasn't there at this point and his role wasn't clearly defined. We'll see if we're able to trade him. He is going to pitch a while longer."
Feliz, who was activated off the disabled list Thursday, finished his Rangers career as a mopup reliever. He came into Friday's game in the seventh and pitched two scoreless innings.
Feliz said he was surprised by the decision.
"Baseball goes on," Feliz said. "There are 30 teams in the league. I'll keep fighting and not hang my head. My mentality is to keep pitching and keep doing my job. Whatever happens, happens."
Despite the two scoreless innings, Feliz still had a 4.58 ERA with opponents hitting .293 off him. He has a 2.73 ERA over the past three seasons since returning from Tommy John elbow reconstruction surgery.
The Rangers just haven't seen the same pitcher who had 72 saves in 2010-11 before moving into the rotation in 2012 and suffering the elbow injury.
"I think he got hurt," Daniels said. "When he had the surgery, he wasn't as electric as he had been before. He had an unbelievably explosive arm … through no fault of his own, he worked hard and came back strong but was not the same pitcher."
Feliz started this season as the closer but lost the job to Shawn Tolleson at the beginning of May. He spent two weeks as a setup/middle reliever before being placed on the disabled list May 20 with an axillary abscess in his right side.
The Rangers did not rush him back. Feliz made 10 appearances on a medical rehabilitation start and had a 7.36 ERA while opponents hit .319 off him. With his rehab assignment almost up, the Rangers activated him Thursday.
Friday was an indication the Rangers weren't ready to use Feliz in a prime-time relief role. Tolleson is entrenched as the closer and Keone Kela and Tanner Scheppers are the primary right-handed setup relievers.
The club also needed a roster spot for Matt Harrison, who has to be activated off the 60-day disabled list Saturday. Harrison doesn't pitch until Tuesday, but he has to be activated within two days of the expiration of his medical rehabilitation assignment.
"We were leaning this way," Daniels said. "We needed a 25-man spot and a 40-man spot."