Carpenter, who won the pole for the Indianapolis 500 in May, finished second in the IndyCar season finale at Auto Club Speedway in Fontana, Calif., last month.
Conway won a Detroit street race in 2013 and won the Long Beach street race in 2011. The two drivers will split time in the No. 20 ECR Chevrolet/Dallara.
Conway walked away from the 2012 season finale at Fontana, saying he was not comfortable racing on ovals. He has been interested in a return to IndyCar on a street-and-road-only schedule.
"We couldn't be happier to welcome Mike Conway to the Ed Carpenter Racing family," Carpenter said in a statement. "My partners, (team manager) Tim Broyles, and I are committed to building an organization based on culture, sustainability, and performance. We are very proud of the group of people we have assembled and bringing Mike into the fold creates an opportunity for us to show even more value to our partners and strengthen our team by competing for victories at every single event in the 2014 IndyCar Series."
Conway said he was looking forward to the opportunity.
"It is great news to be back in IndyCar next year for all the road and street courses," Conway said. "I had a lot of fun this year in the select races that I could do, and I hope that I can continue my success with Ed Carpenter Racing next year."
This will be Conway's sixth IndyCar season. He has four podiums and 18 top-10 finishes in 60 career starts.
"I have a great deal of respect for Ed Carpenter to have the vision to put Mike in the car for the street and road tracks," said Conway's agent, former IndyCar driver Mark Blundell. "I think that the blend of his skill sets on the ovals combined with Mike's talent and pace makes for a very strong combination over the 2014 season."