St Mirren, who are also seeking a buyer for the club, had been without a manager since ending Gus MacPherson's seven-year tenure after his side finished the season in tenth place.
And chairman Stewart Gilmour revealed that Lennon was the only candidate interviewed for the vacancy.
"Danny is one of the up-and-coming managers in Scotland and this is a great opportunity for St Mirren Football Club to give Danny the opportunity to take the club forward," explained Gilmour.
"We would like to thank Cowdenbeath for their co-operation in getting the deal done so speedily."
Whether MacPherson's assistant, Andy Millen, will remain as part of the backroom staff will be decided in the coming days.
Gilmour added: "We are interviewing all the staff and will announce the management team on Friday or Monday."
Asked about the prospect of working with Millen, Lennon said: "I don't have any problem with that. We'll just have to wait for the discussions throughout the week."
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