The deal for the 30-year-old, who previously played in the Premier League at Watford between 2014 and 2017, does not include an option to buy.
Ighalo is due to fly to the UK from China, where he has played for the last three years, over the weekend.
He scored 16 goals in 55 Premier League appearances for Watford before leaving for China and will provide short-term cover for the injured England international Marcus Rashford.
Speaking about Ighalo’s arrival, United manager Ole Gunnar 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.”
Ighalo first moved to Chinese Super League side Changchun Yatai, before he joined Shanghai Shenhua in February 2019.
The striker finished as top scorer in African Cup of Nations qualifying for Nigeria with seven goals, before scoring five at the tournament last summer.
Tottenham made their own late attempt to secure a loan deal for Ighalo on Deadline Day.
Inter Milan also wanted to sign Ighalo, when their pursuit of Chelsea forward Olivier Giroud failed, but the Nigerian had his heart set on a move back to English football with United.
After the home game against Wolves on Saturday, live on Sky Sports, United have a 16-day gap before they play Chelsea in their next Premier League fixture.
United made Bruno Fernandes their first signing of the January window on thursday for an initial fee of around £46.6m to Sporting Lisbon, with potential add-ons taking the overall deal to £68m.