After his first two tracks, Evans said: "Buckle up now guys, but not too tight for it's going to be a long but pleasant ride I promise."
"This time I can guarantee there will be very little, if any, turbulence at all but of course that doesn't mean we're not going to have fun," he said, acknowledging his falls from grace from both the Radio 1 and Virgin breakfast shows.
Evans welcomed listeners to the programme saying: "This is the Radio 2 breakfast show, starring you", and invited fans to call in to discuss anything they were doing for the first time and their plans for the day.
The DJ said he knew Sir Terry was not listening to the show because he was on holiday in France.
However, he revealed the veteran presenter had left a voicemail message for him on Sunday night, which he then played for listeners.
"I just wanted to wish you well. I know you will do a marvellous job - you'll be brilliant," Sir Terry said.
Evans added that he had been sent numerous good luck presents prior to the programme, including chocolates, yoghurts and cakes, plus hundreds of good luck emails and texts from well-wishers.
Chris Evans has presented the Radio 2 drive-time show for three years
His musical choices included songs by Frank Sinatra, Robbie Williams and Madonna.
Speaking on BBC One's Andrew Marr show on Sunday, Evans said he would be delivering the same product as Sir Terry but in a "different way".
He also added he had recorded six practice shows including a full dress rehearsal on Friday in preparation.
Referring to Sir Terry's loyal band of listeners, Evans said it would be a "family show for everyone".
Wake Up to Wogan was the UK's most popular breakfast radio show, with 7.93 million listeners each week.
Sir Terry will host a new Sunday show from February.
He has also just been announced as the chairperson of this year's Oldie of the Year awards which celebrate the efforts of the UK's well-known older stars.
Past winners have included Sir David Attenborough, Tony Blackburn and Eric Sykes.
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