In a Twitter post, Incognito wrote "it's official" and thanked "my family and friends for their continued love and support."
The Miami Herald and ESPN, without naming sources, also reported Incognito's suspension had been lifted by the team in an administrative move.
Incognito was suspended Nov. 3 in the wake of accusations of harassment, intimidation and bullying by Martin.
NFL special investigator Ted Wells is still conducting an inquiry into the club's workplace conduct as a result, which is expected to be released soon.
Martin left the team prior to an Oct. 31 game against Cincinnati.
Incognito has denied bullying Martin but has admitted using harsh and racist language.
Dolphins owner Steve Ross said in an interview last week he does not expect either to play for his team again.