Horst Tappert was born on 26 May 1923 in Elberfeld (now Wuppertal), Germany. His father was a civil servant. Following high school, Tappert was drafted into the German army in World War II and ended up as a prisoner of war. Like the later author of the Derrick series, Herbert Reinecker, Tappert joined the Waffen-SS. Initially a member of the SS-Flak-Ersatzabteilung (Arolsen), he was listed as a member of 3rd SS Division Totenkopf in March 1943. Following the war, he was hired as a bookkeeper at a theatre in Stendal, Germany, and became interested in acting. He took acting classes and gave his stage debut in Stendal, playing Dr. Stribel in Paul Helwig's Die Flitterwochen.

In the late 1950s, Tappert started taking part in movie and television productions. His big breakthrough was in 1966 with the three-part television show Die Gentlemen bitten zur Kasse, in which he played train robber Michael Donegan. In 1968, he changed sides by playing Scotland Yard detective Perkins in Edgar Wallace movies. When the second public television station in Germany, the ZDF, started planning a new mystery series with a different type of investigator in 1973, he was chosen for the character of detective Stephan Derrick, with sidekick assistant Harry Klein (played by Fritz Wepper).

In the following years, he changed employers several times and, in 1956, started working at the Kammerspiele, Munich. An independent actor since 1967, he worked as an actor until he died.

Divorced twice, he last lived in Gräfelfing near Munich with his third wife, Ursula Pistor (married in 1957). He was the father of three children. Tappert enjoyed fishing and hunting. He had a summer holiday home on the coast of northern Norway, a country where he also became a popular visitor as Derrick as well as a private person. Tappert and his wife Ursula had a cabin in Hamarøy municipality in Nordland from 1990 to 2008 when, due to his age and failing health, they had to sell the cabin. His wife Ursula Pistor is also an actor, a graduate of the same acting school in Berlin as Ellinor Hamsun, daughter of Knut Hamsun.

The character of Stephan Derrick became a cult figure. The series was licensed in 104 countries and was popular with the Chinese, Japanese, and Italians (and even Pope John Paul II). The last of 281 episodes was filmed in 1998, when Tappert reached his self-imposed age limit of 75 years for being a television actor.

Tappert died on 13 December 2008 in Planegg, Germany.

In interviews and his memoirs, Tappert did not elaborate on his World War II career, claiming to have served as a company medic in the Wehrmacht, after which he became a prisoner of war. In April 2013 it was revealed that he had joined the infamous 3. SS-Panzergrenadier-Division Totenkopf, then deployed on the Eastern Front, in March 1943. Historian Jan Erik Schulte, an expert on the history of the SS, said that the circumstances of Tappert's membership of the SS and the question of whether he was pressured or coerced into joining remain unclear.