Chelsea had previously appeared close to losing the 18-year-old after Hudson-Odoi handed in a transfer request in January when he had just 18 months remaining on his contract.
Bayern saw a £35 million ($44m) offer for Hudson-Odoi rejected by Chelsea and have retained an interest in the teenage winger.
However, Goal understands Hudson-Odoi’s progress in Chelsea’s first team during the second half of the season has helped to convince him to stay at Stamford Bridge, having sat on contract offers dating back as far as last summer.
His representatives had not reopened talks regarding a new deal since before January, but Goal recently reported that he has been increasingly keen to stay with the Europa League winners.
He could now earn as much as £100,000 a week in his new contract after his value skyrocketed following his impressive performances for Chelsea, in addition to winning his first caps for England.
Hudson-Odoi was, at times, frustrated during the past season under manager Maurizio Sarri, who looks set to depart Stamford Bridge for Juventus in the near future.
The London-born wonderkid did not make his first Premier League start for Chelsea until after he had made his England debut against Czech Republic in March.
However, after then starting four Premier League games in a row, Hudson-Odoi saw his season ended prematurely after he ruptured his Achilles tendon in a 2-2 home draw with Burnley.
Juventus, Real Madrid, Barcelona and Borussia Dortmund had all scouted or discussed a move for the youngster at various points, with the latter asking for Hudson-Odoi to be included in a swap deal for Christian Pulisic before accepting a £57.6m offer in January to sell their U.S. national team winger.
Bayern had showed the most serious interest in Hudson-Odoi, but will now likely have to look elsewhere for high-profile summer signings as the teenager prepares to commit his future to Chelsea.
With Eden Hazard looking set to depart for Real Madrid in a deal which could be worth in excess of £100m, Chelsea have been determined to keep hold of their other wingers.
Hudson-Odoi is keen to take his favoured number 10 shirt from Hazard, having been offered it by Bayern as part of their talks for a deal.
Ruben Loftus-Cheek, meanwhile, is also in talks over a contract renewal as he continues his recovery from a similar Achilles injury to the one suffered by Hudson-Odoi. Both players are likely to be out for a total of six months, but that has not affected Chelsea’s eagerness to renew the pair’s contracts.