He played mainly as a centre-back despite being only 5'11" in a career that lasted 20 years, and made 112 appearances at international level, being Switzerland's second most capped player behind Heinz Hermann. His son, Bastien, is also a professional footballer.
Geiger started playing professionally in 1977 with FC Sion. He played just two matches in his first season but by 1978, he was a first-team regular in the side that went on to win the Swiss Cup in 1980.
In 1981, he signed for Servette FC, who were one of Switzerland's most successful teams at the time, and became an invaluable player for both club and country. He helped the club win the 1984 Swiss Cup, defeating Lausanne Sports 1-0 after extra time in the final, and the league title in 1985. An aspiring Neuchâtel Xamax side acquired his services in 1986, and he helped it win the national championship during the only two seasons he played for them, 1986-87 and 1987-88.
A move to France was on the cards next for Geiger, as he signed for AS Saint-Étienne during the Summer of 1988. He was a big hit and a first-team regular at Stade Geoffroy-Guichard, but opted for a return to Switzerland and Sion, in 1990. During his second spell, he saw the form of his life as he became captain for both club and the country. He lifted the league trophy for the fourth time in his career as Sion were crowned champions in 1991-92.
In 1995, Geiger signed for Grasshopper-Club Zürich, where he finishing his career after a further two seasons, having played 496 Swiss first division matches, with 38 goals.
Geiger's first managerial role was spent with the reserves of Grasshopper, in 1997. He did so well there that he was given the reigns at another old side, Neuchâtel Xamax, in July 1998. At Xamax, he helped develop the talents of Timothée Atouba, Papa Bouba Diop and Henri Camara, and helped the club avoid relegation from the league in his last two seasons.
Geiger quit the club in July 2002 to take over at FC Aarau, but the club were relegated into the second division at the end of 2002-03 and he was given the sack. In December 2003, he was surprisingly named the manager of Grasshopper, but the team fared poorly under him and he was once again fired.
In January 2010, he was appointed as manager of Algerian club JS Kabylie. On 14 December 2010, Geiger resigned from his position. During his time with the club, his most notable achievement was leading the team to the semi-finals of the 2010 CAF Champions League where they lost to eventual champions TP Mazembe.