After mauling over the offer with his family, Whelan has decided to sign for the Edinburgh club.
The 35-year-old has been out of contract after leaving Aston Villa at the end of last season.
He previously spent nine years as a stalwart at Stoke City during their stay in the English Premier League. Prior to that he played for Sheffield Wednesday and Bury after coming through the ranks at Manchester City.
Whelan has 86 caps for his country.