Baker joins current from investment fund Fleming Media where he focused on developing new IP opportunities across multiple platforms.
Joanna Drake Earl, chief operating officer of Current, said: "Current's approach toward the creation of media for and with a young adult audience is unique in both strategy and execution.
"James' exceptional passion and diverse experience make him perfectly suited to oversee those elements, while guiding our operations in the United Kingdom as we continue to innovate both online and on TV. We're thrilled that he's joined the Current team."
Baker has also held several senior positions at BSkyB, which he joined in 1996 as head of programming.
While at BSkyB, he was promoted to controller of Sky One, Sky Two and Sky Three before taking on the position of managing director of Sky Networked Media, with responsibility for web, mobile, interactive TV and broadband content strategy.
Baker said: "As so many other channels battle against the slow incursion of online content and consumption, Current is shaping up to embrace a truly multi-platform future, where online and TV are fully linked, and users are given the opportunity to actively drive the direction of the network.
"This doesn't just provide viewers and web communities with a dynamic and rewarding experience, but also gives enlightened advertisers and commercial partners the opportunity to engage in smart, targeted and fully integrated campaigns -- working directly with the Current production and marketing teams. "
During the inauguration of US president Barack Obama last week, Current was one of the many media outlets using social media to cover the event.