The Faroe Islands international and scorer of the first ever goal at the Ricoh Arena against QPR in August 2005, had been at Port Vale on a non-contract basis.
I'd like to welcome Claus to Highbury and to Fleetwood Town Football Club," said Fleetwood Chairman Andy Pilley to the Blackpool Gazette.
"We know all about him and he is a fantastic professional. "He's a box-to-box midfield player full of the attributes you would want any professional footballer to possess.
"He will be a shining example to the players on, and off, the pitch on how to conduct themselves and play a professional game