The DJ launched his new show by giving three cheers for Moira Stewart, who has returned to the BBC to be the programme's main newsreader.
According to BBC News, Evans then chose to play Beatles classics 'All You Need Is Love' and 'Got To Get You Into My Life' as his first tracks.
The 43-year-old also told listeners that his first show was dedicated "to anyone who has not been able to sleep recently for the right reasons".
Evans was announced as Wogan's replacement for the breakfast slot last September. He recently admitted that he was nervous about his new position, describing it as his "biggest job by miles".
Wogan is to launch a new Sunday show on Radio 2 from February.