Logan was born on 3 April 1972 in Stirling, Scotland. As a schoolboy, Logan had football trials as a goalkeeper for Dundee United and Hearts. He left school at sixteen and began his rugby career with his hometown club Stirling County, making his senior debut at 17.

Logan played for Scotland A. Logan made his Scotland debut in 1992 against Australia at the age of 19. He was in and out of the side before cementing a position in the starting XV at the 1994 Five Nations Championship. He played in the 2003 World Cup. He won 70 caps over a 13-year period, scoring 20 tries in the process. He retired from international rugby union after the 2003 World Cup.

Logan played for the amateur provincial side Glasgow District. In 1996 the professional era began and the side became Glasgow Rugby. He played for the newly professional team in the three matches of the 1996–97 Scottish Inter-District Championship as well as 2 matches in that season’s European Challenge Cup, the European Conference.

In 1997, he joined Wasps for his first season in English rugby. Logan was with Wasps for seven seasons. Whilst at Wasps he helped them win the Anglo-Welsh Cup in 1999 and 2000; he was a replacement in the 1999 final but started and scored a try and a conversion in 2000. He also helped Wasps win the 2002–03 Premiership Final. In 2004, he re-signed for Glasgow before joining London Scottish after a season. He retired from playing in 2005.

Logan dated newsreader Kirsty Young and moved to London, before the couple separated in 1999 after three years. In July 2001 he married television presenter Gabby Yorath. The couple live in Kew, South West London. After undergoing IVF treatment they had twins, who were born on 28 July 2005.

Kenny and his wife are past presidents of the children’s charity Sparks. In 2009, Logan and Sparks joined forces to organise an annual mass-participation event entitled Logan’s Challenge.

In August 2014, Logan was one of 200 public figures who were signatories to a letter to The Guardian expressing their hope that Scotland would vote to remain part of the United Kingdom in September’s referendum on that issue.