Gale, the former captain and head coach, and Pyrah, who spent more than a decade on the Yorkshire playing staff before becoming bowling coach, were among 16 members of staff abruptly sacked last year in the wake of Azeem Rafiq racism scandal.
They were subsequently part of a group of former Yorkshire employees who won a preliminary employment tribunal hearing in June.
Yorkshire's accounts revealed that the club had set aside £1.9 million for compensation and legal affairs, with Gale set to receive a six-figure settlement, according to the Dail Mail.
A Yorkshire statement said: "On the December 3 2021, the Yorkshire County Cricket Club Limited took the decision to dismiss its coaching and medical staff. The club has acknowledged that its dismissals of that group of employees was procedurally unfair.
"After meaningful dialogue between the club and the legal advisers acting on behalf of Andrew Gale and Richard Pyrah the parties can confirm that acceptable terms of settlement have been reached.
"The financial terms of the settlements are confidential and no further public statement will be made about the terms."
Yorkshire have also reportedly agreed an out-of-court settlement with Ian Fisher, the club's former strength and conditioning coach.