Monahan, 47, has been the tour's deputy commissioner since 2014 and working for the tour in some fashion for the past eight years.
"Jay has proven himself to be an outstanding leader who has developed an intimate knowledge and understanding of the PGA Tour and a clear vision for the future of the organisation," said policy board chairman Victor Ganzi.
His move into the role had been expected. Just as Finchem before him, he served as deputy commissioner and was appointed the tour's chief operating officer before taking the top job.
"I am greatly honoured by the trust the policy board has shown in me," Monahan said.
"Under Tim's leadership, the PGA Tour has made remarkable progress, even in the most difficult economic times.
"We're now entering a very important time in our organisation's history and I know our executive team and I will draw upon and be inspired by the invaluable experience of working with Tim as we take advantage of the extraordinary opportunities, as well as face the challenges, that are ahead."
