Yeboah was born in Kumasi, Ghana. After spending his youth in Kumasi, Yeboah joined German club 1. FC Saarbrücken in 1988. This move was of some historical significance, because Yeboah became one of the first black players to appear in the Bundesliga. Yeboah had a slow first year, but then scored 17 league goals in his second Saarbrücken year.
Eintracht Frankfurt
He was transferred to Eintracht Frankfurt in 1990, where he was at first booed by a section of fans and—being the first black player the team had ever signed—subjected to monkey-noises and other racist insults. In the Hesse metropolis, Yeboah quickly established himself as a deadly striker, silencing all critics, and became the first African Bundesliga club captain. He was the top Bundesliga scorer twice with Eintracht, in 1993 and 1994.
Leeds United
Yeboah joined English club Leeds United from Eintracht Frankfurt for £3.4 million in January 1995. In his second season at Elland Road he was voted Player of the Year. Yeboah scored a total of 32 goals for Leeds United in 66 appearances, and is still revered as a cult hero for the Yorkshire club due to a series of memorable goals he scored. His volley against Liverpool and his strike versus Wimbledon in the 1995–96 season were among his most notable goals, and he was a regular feature in Goal of the Month in the Premier League. He told Newstalk's Team 33 in 2014 that his favourite goal was the one he scored against Liverpool. The goal against Wimbledon was awarded Goal of the Season in 1995–96. Until Gareth Bale equalled the feat in 2013, Yeboah was the only player ever to win successive BBC Match of the Day Goal of the Month competitions, doing so in September and October 1995. He also scored three hat-tricks for Leeds; the first against Ipswich Town in the Premier League at Elland Road on 5 April 1995, which made him the second foreign player to score a league hat-trick for Leeds, three months after Phil Masinga became the first foreign player to score a hat-trick for the club when he found the net three times in an FA Cup tie. Yeboah's second hat-trick came against Monaco in the 1995–96 UEFA Cup on 12 September 1995, and the third 11 days later in the Premier League match against Wimbledon at Selhurst Park which included the aforementioned Goal of the Season. A video was released named ‘Yeboah – Shoot to Kill’ while he was at Leeds. Injuries restricted his game when he played and kept him out of the Leeds side on several occasions. When George Graham took over as manager, there was a clash of personalities and Yeboah was sold to Hamburger SV in September 1997, having played just six times under Graham.
Later career
Yeboah joined German club Hamburger SV and remained there until 2001, scoring 28 goals, in order to join Al Ittihad, where he played under Austrian coach Josef Hickersberger.
International career
He was a member of Ghana's national team for over ten years, and represented his country at three Africa Cup of Nations during the 1990s. Yeboah scored 29 goals in 59 appearances for Ghana, the third highest goalscoring total in the nation's history behind Abedi Pele and Asamoah Gyan.
Yeboah runs an international sports agency called Anthony Yeboah Sportpromotion and owns a chain of hotels in Ghana called Yegoala. He is married and has two children. His nephew, Kelvin Yeboah, is also a professional footballer and plays for Austrian Football Bundesliga side WSG Swarovski Tirol.