Drennan is from a musical family and was born in Luton, England: he and his family moved to Ireland while he was at a young age. He grew up in County Dublin and attended Kilmacud National School.
Drennan was chosen as the touring second guitarist/bassist for Genesis on their 1998 Calling All Stations tour (replacing long-time live band member Daryl Stuermer), and subsequently became a touring lead guitarist for The Corrs from 1999 onwards. In 2010 he was hired as a member of the revived Mike + The Mechanics. He has also played with Clannad, Paul Brady, Moving Hearts, Davy Spillane, the Liffey Light Orchestra, The Ronnie Drew Band and other well-known Irish bands and performers.