The 28-year-old left Tottenham for Premier League rivals Everton on transfer deadline day on a three-year contract.
Lennon played on loan for Everton from Spurs during the second half of last season and did relatively well.
The former Leeds United winger scored two goals and created 14 chances in 14 Premier League appearances.
The England international had a pass accuracy of 78% and a shot accuracy of 71%, and won three headers, nine dribbles and 20 tackles.
Lennon has revealed that he wanted to join only Everton in the summer transfer window despite interest from other clubs.
"There were other clubs interested but to be honest I didn’t really even entertain it," the 28-year-old told Everton’s official website. "Everton was the one for me, it was the one I was waiting for regardless of anything else.
"Honestly, I just sat their hoping this deal would go through, and thankfully it did. From the loan spell you have a feeling of what you want and I was willing to wait until the very last day, the very last hour for this one to happen.”
Lennon is going to enhance the quality of the current Everton squad and will be looking to play an important role in the Toffees’ aim to finish in a European position in the Premier League table.
The former Leeds winger must be hungry for playing time and to prove to his detractors that he can still succeed in the Premier League.