Dailey was born on December 14, 1915, in New York City, to Daniel James Dailey Sr. and Helen Theresa (née Ryan) Dailey. His younger sister was Actress Irene Dailey.

He appeared in a minstrel show in 1921, and later appeared in vaudeville. He worked as a golf caddy and shoe seller before his first big break, working for a South American cruise line in 1934.

He made his Broadway debut in 1937 in Babes in Arms. He followed it with Stars in Your Eyes and I Married an Angel.

Dailey was the Juvenile lead in The Captain Is a Lady (1940) and Dulcy (1940). He appeared in a musical comedy in Hullabaloo (1940), then had a small role in the drama Keeping Company (1941) and was the Juvenile in The Wild Man of Borneo (1941). He could be seen in Washington Melodrama (1941) and Ziegfeld Girl (1941), and played a gangster in The Get-Away (1941).

Dailey was loaned out to 20th Century Fox for Moon Over Her Shoulder (1941), then appeared opposite Donna Reed in Mokey (1942). He was third billed in Sunday Punch (1942).

Dailey married first wife Elizabeth in 1942. They had one son, Dan Jnr, born in 1947, and separated in 1949. They divorced in 1951.

He served in the United States Army during World War II, and was commissioned as an Army officer after graduation from Signal Corps Officer Candidate School at Fort Monmouth in New Jersey. During his army Service, he appeared in This Is the Army (1943).

When Dailey returned to Hollywood MGM agreed to let him sign a contract with 20th Century Fox. Their association began brilliantly with Mother Wore Tights (1947) in which Dailey supported the studio's biggest star, Betty Grable. His part was built up during filming and the movie was Fox's most popular movie of 1947, making $5 million.

Dailey was reunited with Grable in When My Baby Smiles at Me (1948). It was Fox's biggest hit of the year and garnered Dailey an Academy Award nomination for Best Actor.

In 1949, he showcased his singing abilities by recording four songs for Decca Records with the popular Andrews Sisters singing trio. Two of the songs were Irish novelties ("Clancy Lowered the Boom!" and "I Had a Hat (When I Came In)"). The other songs, Take Me Out to the Ball Game and In the Good Old Summertime capitalized on the success of two MGM blockbuster films of the same names from that same year, starring Gene Kelly, Esther Williams, Frank Sinatra ("Tale Me Out to the Ballgame" and Judy Garland and Van Johnson ("In the Good Old Summertime"), respectively. Dailey and The Andrews Sisters were an excellent match, and their vocal stylings on these selections were full of gaiety and fun.

As the musical genre began to wane in the late-1950s, he moved on to various comedic and dramatic roles on television, including starring in The Four Just Men (1959–60).

Fox tried Dailey in a romantic drama, I Can Get It for You Wholesale (1951), playing opposite Susan Hayward. Then he was in a biopic, The Pride of St. Louis (1951) as the baseball player Dizzy Dean.

Dailey made a second film with Ford, a remake of What Price Glory (1952), where he teamed with James Cagney.

Universal borrowed him for a musical, Meet Me at the Fair (1953). Fox put him in a drama, Taxi (1953), then a musical with June Haver, The Girl Next Door (1953). He did another baseball-themed film, The Kid from Left Field (1953).

Dailey was meant to appear in the 20th Century Fox musical extravaganza There's No Business Like Show Business (1954), which featured Irving Berlin's music and also starred Monroe, Ethel Merman, Mitzi Gaynor, Johnnie Ray, and Donald O'Connor, whose wife Gwen divorced O'Connor and married Dailey around that time. Filming was delayed due to an illness to Director Walter Lang, so Dailey was going to appear in Susan Slept Here and Heller in Pink Tights. Susan ended up being made with Dick Powell and Pink Tights was postponed. Eventually There's No Business Like Show Business was made and proved to be Dailey's biggest hit in a long time.

Dailey went to MGM to play GI-turned-advertising man Doug Hallerton in It's Always Fair Weather (1955) alongside Gene Kelly. The film was screened at drive-in theaters and was not a box-office success, although it did receive good reviews.

Dailey returned to Fox for one more musical, The Best Things in Life Are Free (1956) to play Songwriter Ray Henderson opposite Gordon MacRae.

He was one of several stars in Fox's comedy Oh, Men! Oh, Women! (1957). For the same studio, he was part of the ensemble in The Wayward Bus (1957). Dailey made a profitable low-budget war film for MGM, Underwater Warrior (1958).

In the late 1960s, Dailey toured as Oscar Madison in a road production of The Odd Couple. co-starring Elliott Reid as Felix Unger and also featuring Peter Boyle as Murray the cop. He did a stint on Broadway in Plaza Suite.

From 1969-71, Dailey was the Governor opposite Julie Sommars's J.J. in the sitcom The Governor & J.J. which revolved around the relationship between his character, the conservative governor of an unnamed state and his liberal daughter Jennifer Jo. His performance won him the Golden Globe for Best Actor in a Television Musical or Comedy for performances in 1969, the year that this category was introduced.

He starred in a short lived series Faraday & Company in 1973.

Later film performances included The Private Files of J. Edgar Hoover (1977), as Clyde Tolson.

Dailey broke his hip in 1977, and developed anemia. He died on October 16, 1978, from complications following hip replacement surgery. He is buried at Forest Lawn Memorial Park in Glendale, California.