Birdsall takes up his new post at the ABS in March next year.
Lausanne hopes to have his successor in place shortly after the new year to allow for a period of transition.
Over the last eight years, Birdsall has helped the movement make great strides towards its vision of "the whole church taking the whole gospel to the whole world".
He also oversaw the Third Lausanne Congress on World Evangelisation: Cape Town 2010.
Ram Gidoomal, Chairman of The Lausanne Movement Board of Directors, paid tribute to Birdsall: "Together Doug and the global leadership of Lausanne have established a firm foundation for the movement's continued growth and success to the glory of God."
Commenting on his appointment to the ABS, Birdsall said: "The Third Lausanne Congress: Cape Town 2010 renewed a passion in my heart to eradicate Bible poverty and see God's word spread far and wide."
Gidoomal continued: "As Doug moves into this new role he takes with him the prayers and high esteem of the Lausanne Board and the entire Movement. We ask for your prayers as Lausanne's Leadership Selection Committee seeks the Lord's guidance. We are confident God will provide the right leader to take us into the next decade of effective ministry."
Reverend Billy Graham, founder of The Lausanne Movement, said he was very happy to hear of Birdsall's appointment as the new president of the American Bible Society.
"Under his leadership the Lausanne Movement has been strengthened and revitalised, and I pray that God will continue to use it to call the global Church to a renewed commitment to world evangelisation. May God bless the American Bible Society under Doug's leadership as it explores new ways to bring God's Word to this generation."
Birdsall has had a long history of involvement with the Lausanne Movement, starting in 1987 when he was a participant in the Younger Leaders Conference in Singapore.
He has been a member of the Lausanne Board since 1999, and assumed the chairman and chief executive post in 2004.
ABS Board Chairman Pieter Dearolf said Birdsall's new appointment with the organisation "builds on Doug's 30 years of leadership which have been focused on pointing people to the message of the Bible".
He said: "We are excited to have found someone so well-suited for guiding the ministry into a new century of work around the world."