It will be the first time Williams, 42, has written with his former bandmates since 2010 and the tracks will feature on the group's mammoth Greatest Hits album, which will come out next year to mark their 25th anniversary, reported Contactmusic.
"Robbie loves being part of the creative process and he has lots to offer. He influenced the last album he featured on with his electro sound, which reflected his solo work at the time," a source said.
"He's a changed man since studio sessions back in the day and takes things far more seriously," the source added.
In February, Gary Barlow confirmed that the band would tour in 2017 to mark their 25th anniversary.