He studied at the University of Glasgow. 
Glenn joined BBC Scotland in 2001, originally working for their radio station, BBC Radio Scotland. Currently, he works for their television arm, regularly reporting and presenting on Reporting Scotland and Scotland 2016. He also presented the network's coverage of the 2007 Scottish Election and contributes regularly on Good Morning Scotland. 
He has been a stand-in presenter on Radio 4's PM program. Campbell hosted BBC Scotland's coverage of the 2015 General Election and anchored coverage of the 2016 Scottish Parliament Election. 
On August 25 2014, Campbell moderated the second Scottish independence debate between Alistair Darling and Alex Salmond in Glasgow. He then hosted the Referendum result programme on BBC One Scotland on the night of September 18, 2014.