Former Watford star Ighalo arrives at Old Trafford from Chinese Super League outfit Shanghai Greenland Shenhua on a temporary basis until the end of the season.
The Nigeria international scored 16 goals in 55 Premier League for the Hornets, before joining Changchun Yatai for £20m two years ago.
Solskjaer scoured the transfer market for a striker after Marcus Rashford was ruled out for three months with a back injury sustained against Wolves.
Speaking about the loan deal, Solskjaer said: “Odion is an experienced player. He will come in and give us an option of a different type of centre-forward for the short spell he’s staying with us.
“A great lad and very professional, he will make the most of his time here.”
The 30-year-old lifelong Manchester United fan failed to scored with his last 28 shots before departing the Premier League.
United supporters will hope he will be more efficient in front of goal once he makes his debut.
Ighalo began his professional career in his native Nigeria with local clubs Prime and Julius Berger, before sealing a transfer to Norwegian side Lyn in 2007.
A year later, a move to Udinese in Italy eventually led to loan spells with Granada (twice), Cesena and Watford in the Premier League.
While at Vicarage Road with the Hornets, Ighalo impressively scored 40 goals from exactly 100 appearances across all competitions.
During that time he made three appearances against United and one at Old Trafford, losing twice and winning once, while also earning an assist.