He told BBC Radio 4's Today programme the technology had been used to "extricate" John Lennon's voice from an old demo so he could complete the song. "We just finished it up and it'll be released this year," he explained.
Sir Paul did not name the song, but it is likely to be a 1978 Lennon composition called Now And Then.
It had already been considered as a possible "reunion song" for the Beatles in 1995, as they were compiling their career-spanning Anthology series. Sir Paul had received the demo a year earlier from Lennon's widow, Yoko Ono.
It was one of several songs on a cassette labelled "For Paul" that Lennon had made shortly before his death in 1980. Lo-fi and embryonic, the tracks were largely recorded onto a boombox as the musician sat at a piano in his New York apartment.