The 19-year-old sought a move away from Stamford Bridge in January, after growing frustrated with a lack of playing time under Maurizio Sarri.
Bayern Munich were reportedly very keen on luring the talented winger to the Allianz Arena, but Chelsea were unwilling to sanction his departure.
The German champions submitted a bid of £22.5 million ($29m) in June, which the Blues rejected, with Lampard drafted in to replace Sarri a month later.
Hudson-Odoi eventually performed a U-turn regarding his future, penning a new long-term contract with Chelsea worth £180,000 per week in September.
After recovering from an Achilles injury which had kept him out of action since April, the England international has emerged as a regular in Lampard's line up.
He has now explained that the 41-year-old manager's return to the Bridge helped him make up his mind to continue his development at Chelsea and snub a move to Bayern.
"Him coming here is a big feeling for all of us because he was talking before about how he likes young players and I had an idea in my head that if he comes here it will be great for us," Hudson-Odoi told BT Sport.
"As soon as he came I thought: ‘yep this is it’. I had a few chats with him and thought this is perfect, I want to stay here."
The teenager has contributed three assists in five Premier League outings this term, while also featuring in three Champions League fixtures, impressing Gareth Southgate enough to earn an England recall this week.
Hudson-Odoi could add to his two Three Lions caps in upcoming Euro 2020 qualifiers against Montenegro and Kosovo, before returning to the Bridge to compete for a spot in Lampard's line up after the international break.
The attacker came off the bench to replace Christian Pulisic for the last 10 minutes of Chelsea's 2-0 home win over Crystal Palace on Saturday afternoon.
The Blues will be back in Premier League action on November 23, when they travel to the Etihad Stadium to face reigning champions Manchester City.