It will be 32-year-old Kate's second child, after four-year-old Lila Grace with her ex, publisher Jefferson Hack.
Pete, 27, has a three-year-old son, Estile with former partner Lisa Moorish.
Phil said he spoke to Doherty on Friday when the singer called him from Italy, where he is performing with his band Babyshambles. The rocker told him Kate had had a scan, everything was fine so they were happy to share the news.
Phil said: "They are both delighted and Pete sounded really excited."
Kate, who has been relaxing in Italy with drug addict Pete, is expected to make an official announcement in weeks.
Phil, 57, Pete's favourite uncle, added:
"That is why they want to get married. Pete told me they want a baby together to cement their marriage.
"I am made up for them. I wish them every success. They're so happy, they love each other. I can't wait for the wedding - we are just waiting for a date."
Two weeks ago, the Sunday Mirror revealed Kate, estimated to be worth £25 million, and Pete were trying for a baby.
Pete rejoined his bandmates for the gigs in Italy after quitting the British tour earlier this month following orders from Kate - known as "The Millionairess" by his close friends.
Heroin and crack addict Pete - who had just finished a successful month-long stint at the Priory Clinic in Southgate, North London - had started using again.
He was spending up to £500 a day on drugs. As a result, Kate told him to pull the plug on the tour so he could continue rehab with her at his side - away from the druggie lifestyle on the road. Those concerts have been rescheduled for next month.