Having broken through into the Sunderland set-up as a central midfielder, Mumba has mostly played at right-back in the U23 side during his time on Wearside.
His sale was expected to land Sunderland around £350,000 initially, though a number of add-ons could see the deal rise above £750,000.
A number of senior club figures at the time suggested that Mumba’s contractual status was behind his sale.
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The youngster had one year to run on his first professional deal before signing for the Canaries in July 2020.
Mumba won promotion to the Premier League with Norwich City last season but has found game time hard to come by.
But now, the 20-year-old South Shields-born player has joined Championship outfit Peterborough United after their promotion from League One last season.
Speaking to Posh’s website, Mumba said: “I am really happy to be here and can’t wait to get started.
"My experience at Norwich City so far has been really good and this is an opportunity for me to go out and play first-team football and try and help Posh achieve their targets this season, which is remaining in this division.
“I like to get forward and support the attacks and obviously do my job of defending and I can play in either full-back or wing-back position.
"When I found out about the interest, it was something that really interested me, the manager here has been very successful, the team got promoted last season and I know there are some good players here.
“I just want to meet the lads, get the first training session under my belt and take it from there.
"I know this is a good club, I have spoken to people who have either worked or played here and it is a really good opportunity for me to hopefully play regular first-team football.”
Manager Darren Ferguson added: “I am very happy to get Bali signed. He is comfortable at both left and right-back and can also play as a wing-back. He will be an important addition to the squad, and I am really looking forward to working with him for the rest of the season.”