The 24-year-old initially joined the senior staff on a three-month deal in June 2017 before signing a one-year contract at the end of last summer.
In 2018, he made his Nottinghamshire debut against Somerset in June, playing in six First Class matches and taking 11 wickets with a best of 4-44 against Essex, including the wicket of Alastair Cook.
“I’m grateful for the opportunity that Notts have given me and I have loved every second of being involved with my childhood Club,” said Milnes.
“I appreciate all the help I have been given to improve my game but feel the time is right for me to move on and I’m looking forward to getting going down at Kent.”
Nottinghamshire Director of Cricket Mick Newell is disappointed to see Milnes leave the Club but wishes the fast bowler all the best moving forward
“We are sad to see Matt go but understand the cricket reasoning behind his decision,” said Newell.
“We were pleased with his progress this summer and had offered him a new deal, but he moves on with our best wishes for the future.”