"I feel I have plenty of football left in me and this will be a good place to play," said Andrews, who has won over 100 caps for his country.
Meanwhile young Wrexham centre-back Kai Edwards has joined hometown club Prestatyn on loan to gain experience.
"I'm looking forward to the challenge," said the Wales Under-21 international.
Andrews continues a strong Wrexham tradition of recruiting Trinidad & Tobago stars.
"I was with Dennis Lawrence last week, and he urged me to take this chance and join Wrexham," Andrews told the Wrexham website.
"I grew up with Hector Sam, while also knowing both Carlos Edwards and Silvio Spann very well, and they all told me to sign."
The Dragons need to secure international clearance for Andrews, meaning he will not feature in their season opener at home to Cambridge United on Saturday.
Source: BBC Sport
Source: BBC Sport