The 30-year-old was a free agent after leaving the Pars, who were relegated from the Clydesdale Bank Premier League last season.
Dundee boss Barry Smith told the club's official website, www.dundeefc.co.uk: "Once again we are delighted to have a player with Mark's experience and ability join us. He has proven himself as a quality footballer at the highest level in the past and we are sure he will do so once more at Dundee FC."
Kerr has become the eighth signing at Dens Park since the Dark Blues were formally confirmed as Rangers' replacements in the SPL, ahead of Dunfermline.
- Clydesdale Bank Premier League