The Braves, seeking a veteran reliever after Jason Grilli’s season-ending injury, agreed to terms Wednesday with right-hander Jason Frasor, a person familiar with the situation said.

The move came three days after Frasor was released by the Royals despite a 1.54 ERA in 26 appearances.

The Mariners and Red Sox were among the teams that expressed interest in Frasor, 37, after he was designated for assignment July 3 by Kansas City, a move that surprised many Royals fans and industry insiders.

The Royals DFA’d him to open a roster spot for outfielder Paulo Orlando, and 10 days later Frasor became a free agent after going unclaimed on waivers.

His ERA with the Royals was outstanding and Frasor allowed just one home run, though his strikeouts-to-walks ratio wasn’t good, with 18 strikeouts and 15 walks (two intentional) in 23 1/3 innings.

He’ll provide the Braves with additional experience, after they lost closer Grilli to a ruptured Achilles tendon last week and moved Jim Johnson to closer (and with the possibility that Johnson could be traded by July 31). In Frasor, the Braves were able to add an effective veteran without having to give up anything in a trade.

The Braves will pay him a prorated portion of the major league minimum $507,000 salary, while Royals are on the hook for the rest of his $1.25 million salary and $550,000 buyout of $2 million option for 2016.

In 12 major league seasons, all in the American League, the 5-foot-9 Chicago native is 35-35 with a 3.52 ERA and 35 saves in 673 relief appearances, with 611 strikeouts and 280 walks in 642 innings.

Frasor was 7-3 with a 2.50 ERA and 11 saves in 61 appearances for Toronto in 2009. He pitched for the Blue Jays from 2004 until being traded to the White Sox in July 2011.

After the Royals got him from the Rangers in a July 2014 trade, Frasor posted a 1.53 ERA in 23 appearances during Kansas City’s stretch drive, with 16 strikeouts and only four walks in 17 2/3innings. He also posted a 1.69 ERA in seven postseason appearances for the American League champions, including three World Series games.

For the entire 2014 regular season, Frasor had a 2.66 ERA in 61 appearances, with 46 strikeouts and 18 walks in 47 1/3 innings.