Solskjaer was announced as the replacement for Jose Mourinho who was relieved of his duties as Manchester United boss after a disappointing start to the season.
Now retired, Odemwingie previously played for Solskjaer during his time playing for Premier League outfit Cardiff City in 2014.
During their time together at Cardiff, Odemwingie moved to Stoke City but his former teammates were led to relegation and Solskjaer was sacked when they dropped to the Championship.
Odemwingie made his prediction when interviewed by the BBC, and backed his former manager to succeed at Old Trafford.
When asked on his former manager he said, “Yes, I had a short spell with him what caught my eye was the excitement he had to come and manage in the Premier League.
“He looked really enthusiastic about it, and also he did not come across a defensive minded manager.
“In the week I spent with him before I moved to Stoke City, I felt he was going to be playing more attacking than defensive football which we were doing at the moment.
“They still got relegated but he inherited a squad where he couldn’t spend a lot of money.
“So now he can he will have different kinds of players, so he can properly play the type of football he has in mind.”
Solskjaer is a club legend at Manchester United where he spent about 11 years and won lots of trophies.
He will lead Manchester United in his first match away against his former team Cardiff City on Saturday, December 22.