Following the arrival of midfielder Michael Keane from Preston last week, Southend centre back Cort is the next to join up with the Division Three runners-up.
He will sign a two-year deal when his contract with the Shrimpers expires at the end of the month. No transfer fee is necessary.
The 24-year-old will compete with Damien Delaney, Marc Joseph, Justin Whittle and Richard Hinds for a place at the back.
Peter Taylor is also hopeful of bringing in 30-year-old midfielder Junior Lewis, who can provide cover for the centre backs as well. He played 13 times on loan for City at the end of the season before being released by Leicester, but Taylor says he'll have to agree to a wage cut if he's to sign a permanent deal.