Dickenson, 23, scored four goals in 78 appearances for the Gills across two seasons after joining from Brighton.
He was released by the League One side in May and joins on a two-year deal.
Ex-Millwall trainee Peter, 19, has signed a one-year deal after spending the season half of 2015-16 on trial with the U's Under-21 side.
He will be available for both the under-21 side and first-team as John McGreal makes his fifth and sixth signings since becoming U's boss.
Forward Denny Johnstone, midfielder Courtner Senior and defenders Luke Prosser and Ben Wyatt have all joined.
Find all the latest football transfers on our dedicated page.
Colchester United have signed former Gillingham versatile left-back Brennan Dickenson and ex-Chelmsford City centre-back Dexter Peter.