Gilmour said the tour is set to begin April 4 at Radio City Music Hall in New York.
"I've had a fantastic time making 'On an Island' and really want to perform tracks from it, along with my more familiar repertoire," he said.
"On an Island" will be released in March. The title track teams Gilmour with David Crosby and Graham Nash.
"I'm rather hoping that with this tour announcement people will believe me when I say, `Honestly, this is the only band I plan to tour with!'" the 59-year-old entertainer said.
Pink Floyd reunited this summer for a Live 8 benefit concert in London. It was the first time Gilmour, drummer Nick Mason, keyboard player Richard Wright and bassist Roger Waters had appeared onstage together since a concert at London's Earl's Court in 1981.
Gilmour's tour also will include performances in Toronto (April 9-10), Chicago (April 12-13), Oakland, Calif., (April 16-17) and Los Angeles, (April 19-20).