The 30-year-old is expected in Saudi Arabia on Friday to complete a £51m transfer, with Villa poised to finalise the signing of Chelsea's Nicolas Jackson for £65m as his replacement.
Emery praised Watkins' conduct throughout his six years at Villa Park and confirmed that he and the squad had accepted the forward's apology after he made himself unavailable for Sunday's Premier League defeat at Brighton & Hove Albion.
Watkins leaves as Villa's record Premier League goalscorer with 91 goals, part of an overall haul of 108 in all competitions since joining from Brentford for £28m in 2020. He was a central figure in Villa's Europa League triumph in May, and his form this year earned him a place in England's squad for this summer's World Cup.
"He told us after the Brighton match he was sorry and that he had made a mistake. He was wrong, but we accepted it. The players as well," Emery said.
"His commitment and his behaviour was fantastic. He's a fantastic guy - a fantastic guy even more than a player. I told him 'bye' with a huge hug and with small tears.
"But now it's a new chapter here with Nicolas Jackson."
Villa have agreed terms for Jackson and are working to have the Senegal international registered in time for Monday's visit of Arsenal.
Watkins becomes the latest experienced figure to depart Villa Park this summer, and Emery urged supporters to trust the club's strategy despite the exit of several key personnel from last season's successful campaign.
"We took decisions because it's good for the club," Emery said. "Of course, we don't want to be a club that sells players, but the responsibility is there. It's crazy [money for someone] 30 years old and £50m for Ezri Konsa [who is 28].
"How we developed in the last year with some players and how we can sell some players now is completely the right decision. We have to rebuild the team as fast as possible. [Fans] have to accept our way and why we are taking some decisions."
As part of that rebuild, Leon Goretzka completed a free transfer to Villa on Thursday after leaving Bayern Munich at the end of last season. The German midfielder won seven Bundesliga titles and the Champions League during his time in Bavaria.
"He is a winner. He is a very competitive player - a good player to add into our squad," Emery said of Goretzka. "He is versatile and arrives fit and training well. Hopefully on Monday he can be on the field."