Ighalo initially joined United in a temporary deal at the end of the January transfer window as the club sought cover in attack for the rest of the season, with Marcus Rashford suffering a long-term injury.
The signing of Ighalo raised eyebrows, but the former Watford man scored four goals in eight matches in all competitions - starting just three of those games.
The season's suspension due to the coronavirus pandemic in March led to concerns United would lose the services of Ighalo before the conclusion of the 2019-2020 campaign.
But United confirmed they had reached an agreement with Shanghai on Monday, leaving the 30-year-old overjoyed.
"I'm really happy," he told United's official website. "It's a dream for me to be here. I'm buzzing and ready to go.
"I feel okay. The last few days have been difficult as there have been different talks about it but now I'm really happy, so I need to concentrate fully. I'm here until the end of January, so it's good for me.
"I decided I want to stay and I'm happy. Since the first day I arrived, I made it clear that I wanted whatever it takes to continue that work. It was very difficult, there were some talks, but I'm happy they finally agreed and got everything done. Everything is official now.
"I'm sending thanks to the Shanghai president and director for the support because they know this is what I want. So, I'm thanking them and I'm happy that this has happened. They wish me all the best too.
"Like I've said, since I was young, I've been supporting this club and playing for it is a dream. Now I've extended my loan, it makes it more even clear and I'm committed as I know, in my head, I'm here until the end of January
"I just want to work hard and enjoy it, support the team and do whatever I can to make us go higher and higher."
Pending final government approval, the Premier League will resume later this month.
United heads into the final nine league games three points adrift of fourth-place Chelsea, while it is also in the FA Cup quarter-finals and has one foot in the last eight of the Europa League having thrashed LASK 5-0 in their final match before the season halted.