Valentine confirmed the Bogar move during an appearance Wednesday on sports radio WEEI.
Royster, who was drafted by the Dodgers two years after they took Valentine, first posted the news on his Facebook page. Contacted Tuesday night, Royster said he would speak "soon," but that he had "unfinished business."
Bogar, who was the third-base coach under Terry Francona the past two seasons, becomes an obvious candidate to succeed Valentine when his term with the Red Sox ends. Valentine is signed for two years, plus an option. Bogar played for Valentine's Mets in 1996.
"One of my former pupils," Valentine said of Bogar during an ESPN broadcast of a Red Sox game last season. "A very good baseball man and future manager at the big league level, no doubt."
Valentine acknowledged Wednesday on WEEI that his last business interaction with Bogar wasn't under the best of circumstances.
"I guess when I was managing Tim in New York he was traded to the Astros -- or he might have been released and then signed by the Astros -- but it wasn't a pleasant situation," Valentine said. "But since then we've had a relationship where I've seen him in the dugout or I've seen him on the field and I've always admired his passion for the game of baseball and his knowledge of the game of baseball."
When pressed on details of the Bogar move from the Mets, Valentine added with a laugh: "What I have to do is look up the facts and see if it was a release or a trade, but I remember it was an ugly situation."
The Red Sox have yet to name a pitching coach, but Valentine said Wednesday that they have decided on a candidate and an announcement could be made shortly.
"Basically I've exhausted all friendships, relationships, lists that I've seen of many, many ex-pitchers and pitching coaches that are out there," Valentine said.
He said he and his Red Sox colleagues have "gone through the names, have gone through the interviews and I think that we've come to one mind of who that guy is going to be. It should be announced as soon as [Red Sox GM] Ben [Cherington] gets the contract signed."
A major league source said they were giving serious consideration to former big leaguer Neil Allen, who managed Tampa Bay's Triple-A team last season, but a Red Sox source shot down that possibility Wednesday morning.
Also Wednesday, ESPN's Jeremy Schaap reported that former Boston first baseman Bill Buckner will join the Cubs' Class A affiliate Boise Hawks as their hitting coach -- ending speculation that he could be hired to join the Red Sox coaching staff. Buckner makes his home in Bosie, Idaho.
DeMarlo Hale, who became Boston's bench coach when Brad Mills was hired to manage the Houston Astros before the 2010 season, has gone to the Baltimore Orioles as their third-base coach after he was not interviewed prior to Valentine's hiring.
Royster and Valentine never played together in the Dodgers' system, except in spring training. Valentine made it to the big leagues with the Dodgers in 1972 but was traded to the California Angels a year later, when Royster made his big league debut with the Dodgers.
Royster, an infielder, played for five teams in 16 seasons, 15 of which were spent in the National League. He retired just before his 36th birthday, then became a minor league coach, instructor and manager before returning to the big leagues as the third-base coach for the Colorado Rockies in 1993, their inaugural season.
He coached third for the Milwaukee Brewers before replacing Davey Lopes as manager two weeks into the 2002 season. He was fired at the end of the season.
Royster also spent three years managing the Lotte Giants in South Korea, becoming the first foreigner to manage in the history of the Korea Baseball Organization.
Gordon Edes covers the Red Sox for ESPNBoston.com. ESPNBoston.com's Joe McDonald contributed to this report.