The club have struggled following relegation and have won just once in the National League North so far this season.
Jenkins, who left to take over at Boreham Wood in the summer, was out of work after being replaced by a former manager himself earlier this month when Luke Garrard returned.
Cox departs after nine league matches, Tuesday night's 4-1 loss at Leamington their fifth defeat inside the first two months.
“It’s a club that I know inside out with a hugely talented group of players,” Jenkins, who took Oxford to promotion in 2023, told the club’s website.
“Results haven’t gone their way so far but we will work hard and that will turn - there is still a long way to go this season. I can’t wait to get started.
“We have a massive game in the FA Cup on Saturday so I’ll take training today, talk to the players, and then all of our energy will go in to getting this club back to where it belongs.”
Owner Justin Merritt said: “It’s never easy to part company with a manager. Sam is a very talented coach who was the outstanding candidate in the summer. His philosophy aligned perfectly to Oxford City matched with an inspiring personality.
“Ross is an outstanding manager who knows the club, the players and will come in and hit the ground running from day one.
“His knowledge, professionalism and desire to achieve are exactly what we need coupled with an extensive network within the game. I am excited about the opportunity to work with Ross again.”