The 31-year-old centre-back made 131 appearances for the O's after moving to east London from Huddersfield Town in the summer of 2012.
"While playing here I have been away from my young family. I feel living apart has become too hard," he said.
"I have on many occasions put the club before my family's happiness and that should never happen."
Clarke, who had a year remaining on his contract at the Matchroom Stadium, said the decision to leave the club had "not been easy".
"I would like to start by saying how proud I have been, being captain of this football club," he added in a statement on the Orient website.
"I would also like to thank the manager [Ian Hendon] for understanding my reasons and supporting me.
"In my time here I have had unbelievable support from the fans and I hope they could see I gave everything for the team."
Leyton Orient captain Nathan Clarke has left the League Two club in order to move north and be closer to his family.