Matt Herges, the Giants’ bullpen coach for the past two seasons, is moving up and out.

The Diamondbacks will name Herges their pitching coach, a major-league source confirmed to The Chronicle on Wednesday night.

Herges becomes the first of Bruce Bochy’s coaches to find other work. Others are expected to follow. as the Giants prepare to hire a new manager who figures to bring in many of his own coaches.

The formal announcement in Arizona is expected Thursday.

President of baseball operations Farhan Zaidi told the coaches over the season’s final week that they were free to look for other jobs, as the staff would not be settled until a new manager was on board.

Herges, 49, coached a San Francisco bullpen that tied the division-winning Dodgers for the best ERA in the National League in 2019 at 3.85. The Giants’ bullpen ranked sixth in 2018 at 3.79.

Herges pitched for Arizona in 2005. In fact, the pitched for every National League West team, including the Giants from 2003 until they traded him to the Diamondbacks in June, 2005.

Now, he will coach for this third NL West team. He was the Dodgers’ Triple-A pitching coach in Oklahoma City before the Giants hired him as bench coach.

The Arizona Republic first reported Herges’ hiring Wednesday evening.

Henry Schulman is a San Francisco Chronicle staff writer. Email: hschulman@sfchronicle.com Twitter: @hankschulman