The 38-year-old former club captain said: "I have a very good working relationship with Peter and I would like to make the point that I probably wouldn't be here if it wasn't for him," the former Northern Ireland internationalist said.
"I had offers last year to go to England and work but Peter convinced me to stay on.
"He saw potential in me and made me feel I was an important of the club so I owe Peter a lot.
"The board kept me abreast to the comings and goings. As the time went on I was anxious but when I was told I was told I was getting the job I was relieved but delighted."
Lennon added: "I'm confident. It's a priority to challenge for the title as it is every season. As a player I knew how to get it done, I've done it once as a coach, albeit over eight or nine games under Gordon Strachan.
"I know last season wasn't good enough but the players showed me in the last eight or nine games that they do have it in them. But I will look to bring a few players in with a bit more experience."