Tredwell had suggested such a move at the end of the 2013 season after becoming a regular in England's one-day side due firstly to Graeme Swann's elbow problems and then when the fellow offspinner was rested. He was also named England captain for a Twenty20 against New Zealand when Eoin Morgan picked up an injury although the match was washed out after two deliveries.
Key was previously in the job from 2005 to 2012 during which time the club secured their most recent trophy with the 2007 Twenty20 Cup. Sam Northeast, the opening batsman, will be Key's vice-captain.
Tredwell said it was not in the best interests of the county to have the uncertainty over when he will be around even though he is not part of England's Test plans. Depending on how Swann's workload is managed next season, Tredwell could feature in the Sri Lanka one-day series in May and then against India at the end of the season.
"It was with great honour that I took on the captaincy role twelve months ago, and it has been a very tough decision to not carry on," he said. "However my increased involvement with the England one day squad over last winter and our summer meant I missed large chunks of time in Kent colours and found this particularly difficult.
"This may or may not be the same going forward, so in the eventuality I may not be around I feel it is in the best interests of our team here at Kent that I stand aside."
Kent's chairman of cricket, Graham Johnson, said: "We respect James' desire to focus on his England career and we thank him for his leadership during the 2013 season. James remains committed to the club and retains his desire to offer leadership in the future.
"In Rob, clearly we have someone with all the attributes required of a captain who has shown a great commitment to the county over a great number of years, and a player who has progressed through the Kent system. Having had a season off from what is a demanding role, he shows a renewed desire for the role and an appreciation of what it will take to develop Kent's on field performance from a squad with much potential.
"Our objectives remain the same, the challenge is to achieve the higher level of performance delivery to which the players and those following Kent aspire."
Kent endured a disappointing 2013, finishing seventh in Division Two of the County Championship, failing to progress from the group stage of the Friends Life t20 and ended fourth in their group in the YB40.