The winner, based on voting by the 15,000 DGA members, will be announced Feb. 7 at the 67th DGA Awards ceremony at the Hyatt Regency Century Plaza.
Key contenders excluded included Ava DuVernay for "Selma," David Fincher for "Gone Girl" and Christopher Nolan for "Interstellar." The nominations for Eastwood, his fourth, and Tyldem were the biggest surprises.
It was the first nomination for Anderson, Linklater and Tyldum.
"Couldn't be more excited to be recognised by my peers," Tyldum said. "I am thrilled that my fellow directors gave me this honor, and to be in this group of talented artists is overwhelming. I am truly over the moon."
Eastwood won the DGA trophy in 1992 for "Unforgiven" and in 2004 for "Million Dollar Baby," and he was nominated in 2003 for "Mystic River." Inarritu was nominated in 2006 for "Babel."
Alfonso Cuaron won the DGA award and the directing Oscar last year for his high-tech space thriller "Gravity." Ben Affleck won the won the DGA award in 2013 for "Argo"even though he did not receive an Oscar nom -- becoming only the seventh DGA winner not to also receive a directing Oscar in the history of the DGA Awards.
Directors make up about 6% of the Academy of Motion Picture Arts & Sciences, which announces its nominations Thursday.
"In a year full of excellent films, DGA members have nominated a stellar group of passionate filmmakers," said DGA president Barclay. "Inspiring and artistic, these five directors made films that left an indelible impact not only on their fellow directors and members of the director's team, but on audiences around the world. Congratulations to all of the nominees for their terrific work."
The DGA will announce its television and documentary nominations on Wednesday.
The full list of nominees and their teams:
Wes Anderson - The Grand Budapest Hotel
Clint Eastwood - American Sniper
Morten Tyldum - The Imitation Game
Richard Linklater - Boyhood
Alejandro González Iñárritu - Birdman