Beausejour joined the Blues in a £4million deal from Mexican side Club America on transfer deadline day.
Beausejour told Radio Agricultura: “I am very happy and proud to get the chance to play in such an important league, the most watched in the world and where the best football is being played.
“I am also very happy to have the chance to arrive at a team that made a very big effort to give me this chance.
“I have signed a very good contract, at this league’s level. All the parts involved are satisfied. I have signed a three-year deal.
“I feel that all that I am getting in my career is thanks to a lot of work and effort. I am arriving at a team that has been watching me for a long time and I am very happy for that.”