Ighalo, who spent the last year on loan at Old Trafford, was unveiled by the Riyadh-based team in a video posted on the club's social media channels.
The Nigeria international had been due to return to Shanghai at the end of the loan deal, which had been extended by United for a further six months after he impressed during his initial spell under manager Ole Gunnar Solsjkaer.
This season, the former Watford striker had become frustrated at his lack of game-time this year limited to one substitute appearance in the Premier League.
"It's so hard to see this dream come to an end," he said on Instagram. "But I give God the glory for helping me fulfil this lifelong dream of putting on a Manchester United shirt as a player and represent this great club, it was indeed an honor I will forever cherish and be grateful for."
He is the latest high-profile foreign player to leave the Chinese Super League following the departure of Brazilian forward Hulk from Shanghai SIPG and former Liverpool, Real Madrid and Newcastle coach Rafa Benitez from Dalian Pro.
The 31-year-old joins an Al Shabab side that already features former Sevilla and Argentina midfielder Ever Banega on their books, and lead the 16-team Saudi Premier League.