The 28-year-old centre-half, who is the brother of ex-Orient loanee Tom, has agreed a two-year contract at Brisbane Road.
Clarke was a free agent having left the Terriers this summer after 11 years and more than 300 appearances for the Yorkshire club.
He becomes Orient manager Russell Slade's seventh summer signing, joining Gary Sawyer, Anthony Griffith, Mathieu Baudry, Michael Symes, Ryan Allsop and Ryan Brunt in east London.
Slade told the club's official website: "We've been chasing Nathan for most of the close season and we're absolutely delighted to have landed him.
"He was well sought after by a lot of football clubs. We've had to be patient and that patience has paid off.
"We conceded 77 goals last year - that was the most I've ever conceded and we needed to do some work on that.
"I feel as if we've improved that unit and we've got competition for places. Nathan is a major signing for us and I'm delighted to bring him in."
