The two clubs announced the deal over the weekend, as the 30-year-old striker ends a successful six-year spell at Villa Park, and he leaves as Villa's top scorer in the Premier League.
Full details of how much the deal has cost were not disclosed, but British media reported the Saudi giants paid £51M for the England international, who had two years left on his Villa contract.
Watkins has signed a three-year contract in Riyadh, as the ongoing squad exodus continues from Villa this summer, and he hinted that an exit was not originally in his plans.
"Firstly, I would like to say, never did I intend, nor did I imagine, my time at Aston Villa would end this way," Watkins posted on social media.
"With that being said, I am eternally grateful for the last six years. Not only has it shaped me as a player, but as a person.
"We've been through so many ups and downs in my six seasons here, but one thing that's never changed is that I have given everything for this club.
"From my first goals in the 7-2 win over Liverpool to getting the club back into Europe, the Champions League nights at Villa Park to that unforgettable night in Istanbul and becoming Villa's record Premier League goalscorer.
"It is an achievement that I never thought would be possible when I signed for the club.
"I want to thank everyone who has contributed to my time here, Dean Smith, Steven Gerrard and especially Unai Emery for always believing in me.
"Birmingham will always be home, and so will Villa."