In 1994, Schwimmer was cast as Ross Geller in NBC's situation comedy Friends, a series that revolved around a group of friends who live near each other in Manhattan. He played a hopeless-romantic paleontologist who works at a museum and later becomes a professor at a university. Schwimmer initially turned down the role as Ross, but accepted afterwards. Executive producer Kevin S. Bright said that he had previously worked with Schwimmer, the character of Ross was written with him in mind, and he was the first actor cast. Schwimmer based Ross on Nicolas Cage's role of Charlie from the 1986 film Peggy Sue Got Married. The show debuted on September 22, 1994, and was watched by almost 22 million American viewers. Friends quickly developed a loyal audience, with the show and Schwimmer receiving strong reviews. The Pittsburgh Post-Gazette was complimentary of Schwimmer, calling him "terrific". Variety's television reviewer, said: "All six of the principals, especially (Courteney) Cox and Schwimmer, appear resourceful and display sharp sitcom skills". For this performance, he earned an Emmy Award nomination in the category of Outstanding Supporting Actor in a Comedy Series in 1995.
Schwimmer starred in his first leading film role in the 1996 romantic comedy film, The Pallbearer with Gwyneth Paltrow. In the film, Schwimmer plays a man asked to deliver the eulogy for a high school friend he cannot remember, and begins an affair with the friend's mother. Critics dismissed The Pallbearer as a poor imitation of the 1967 film The Graduate. Variety's film reviewer complimented the actor, writing that he had enjoyed his performance, stating that he displayed "a winning, if rather deadpan, personality along with good comic timing". It also concluded that Schwimmer had a "promising bigscreen future". Janet Maslin of The New York Times cited that his first film "relegates him to a drab role". When asked why he decided to accept the role, Schwimmer admitted the decision was to "make an effort to find roles that are as far away from the character of Ross as possible". He was offered a role to star alongside Tommy Lee Jones in the 1997 science-fiction comedy Men in Black, but turned it down in favor of starring in The Pallbearer, explaining, "This is an opportunity to grow rather than go for the quick cash".
His next film roles in 1998 were Kissing a Fool, Six Days Seven Nights, and Apt Pupil. In Kissing a Fool, a romantic comedy, Schwimmer played Max, a dapper, smart-mouthed ladies' man. Mick LaSalle of the San Francisco Chronicle wrote, "Fans of the sitcom Friends may be surprised by David Schwimmer in Kissing a Fool. Take it from someone who has never seen Friends and comes at Schwimmer with no preconceptions: He does just fine. As a TV sports reporter in Kissing a Fool, he oozes the command and self-satisfaction of a young, successful man". The film was critically and financially unsuccessful. In Six Days Seven Nights, he played the boyfriend of Anne Heche's character. In Apt Pupil, adapted from a novella of the same name by Stephen King, he had a supporting role as a school guidance counselor. "I was scared of the part", Schwimmer said, "but I wanted to be part of the movie". At the time, he noted it was a "little frustrating" that people would typecast him due to his role on Friends. He subsequently appeared opposite Woody Allen and Sharon Stone in Alfonso Arau's straight-to-cable comedy Picking Up the Pieces (2000).
In 2001, Schwimmer played Captain Herbert M. Sobel in Steven Spielberg and Tom Hanks' HBO World War II miniseries Band of Brothers. The television miniseries is based on the book of the same title written by historian and biographer Stephen Ambrose. Although Band of Brothers was met with largely positive reception, Schwimmer's performance was criticized; the BBC News concluded, "Part of the problem ... may have been the ridiculous fact that Friends favourite David Schwimmer plays the hard and cruel Captain Herbert Sobel. The only thing believable about Schwimmer's acting is when he cowers in the face of true battle. His puppy dog eyes make him appear even more pitiful". Later that year he portrayed Yitzhak Zuckerman in the war drama Uprising, based on the true events of the Warsaw Ghetto Uprising in 1943.
In March 2004, Schwimmer appeared as himself on HBO's comedy series Curb Your Enthusiasm.During the lengthy run of Friends, Schwimmer directed ten of the show's episodes. The show's tenth and final season ended on May 6, 2004.