Ross, who is currently controller of film and drama at Channel 4, will join the National in November to work alongside outgoing artistic director Nicholas Hytner, and will formally become chief executive when Rufus Norris takes over as director in April 2015.
Ross, who has previously sat on the board of the National, succeeds Nick Starr, who steps down as executive director at the end of August 2014. Lisa Burger, the NT's chief operating officer, will continue her role as the third member of the executive.
Announcing Ross' appointment, NT chairman John Makinson said: "Tessa's international experience and reputation as a producer and executive need no introduction, and her partnership with Rufus Norris will give us the strongest possible platform on which to extend the National Theatre's creative and commercial leadership."
Rufus Norris added: "I am both thrilled and honoured that Tessa Ross is coming to join us at the NT, and to be my partner at the helm of this unique organisation. She is an extraordinary woman: a world-class producer, a tireless supporter and promoter of both emerging and established artists, a great manager and businesswoman."
Tessa Ross joined Channel 4 in 2000 and became head of Film4 in 2003, taking over her current position in 2008. During her tenure Film4 has co-produced films including Oscar winners 12 Years a Slave and Slumdog Millionaire. Last year she won a BAFTA for Outstanding British Contribution to Cinema.
"I'm incredibly excited to be joining the National Theatre, one of our most iconic and significant cultural institutions and a place that I've loved since I was very young," Ross said today. "Under Nicholas Hytner and Nick Starr's leadership, it's been an exceptional and inspiring home for the theatrical and creative communities, and I'm privileged to be working with Rufus to build its next chapter."