The 28-year-old defender has penned a two-year deal with the Railwaymen after leapfrogging them into League One.
Robertson revealed his decision was helped by former team-mate Jamie Lowry after his successful loan spell at Gresty Road last term.
"He was full of praise and I think he is desperate to come as well," Robertson told BBC Radio Stoke.
"I was keen to stay in League One. The facilities were fantastic, and I spoke to people I know who were here last season and they were full of praise for the management staff.
"There was the ability of the team as well, they were all big factors for me."