"It's our priority to challenge for the title, but we know we've got to hit the ground running."
Johan Mjallby, Alan Thompson and Garry Parker are expected to form Lennon's backroom team.
However, when pressed on the subject, Lennon said: "There will be no announcements until everything is in place.
"But there are no mixed messages. I will be making all of the decisions on the football side of things."
Stuart Baxter has been approached by the club to act in an advisory capacity to Lennon while retaining his head coach position with Finland.
All Lennon would say on Baxter was "he's a candidate, among others".
However, he reaffirmed that it would be a wise idea to have a more experienced man on hand.
"I've said before that I might need an older head to bounce ideas off.
Reid explains choice of Celtic manager
"It would be churlish to suggest I can do all of this by myself."
The former captain took charge of the team after Tony Mowbray's sacking in March, enjoying a 100% league record.
The only black mark against him was an embarrassing Scottish Cup semi-final defeat at the hands of First Division Ross County.
And despite more high-profile names such as the Republic of Ireland coach Giovanni Trapattoni being linked with the position, Celtic chairman John Reid insisted there was never anyone else in the frame.
"We have spoken to no one, nor offered the job to anyone, other than Neil Lennon," said Reid.
"We have appointed Neil after the most careful thought, deliberation and scrutiny.
"He faced up to the challenge at the end of the season in difficult circumstances, and he did his talking on the park."
Signed by Martin O'Neill, Lennon arrived at Celtic as a hard-tackling midfielder in 2000, winning five championship titles in seven seasons.
He returned to the club in a coaching capacity in 2008 to assist then manager Gordon Strachan.
Following Strachan's exit and Mowbray's subsequent employment last summer, Lennon was kept on but was sidelined to a role with the under-19s.
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