The 21-year-old Barbadian has been given an unexpected chance after Jermaine Lawson pulled out of the side with a bout of chicken pox.
"I am looking forward to going out there and doing my best for the West Indies, it's a great honour," he said.
"It's a perfect opportunity for me to show the Caribbean -- and the world -- my talent," he added.
Best was the leading wicket-taker this season in the 2003 Carib Beer Series, his 39 wickets coming at an average of 18.25.
Best, who toured Britain and Canada with the West Indies 'A' team last summer, was due to leave Barbados on Wednesday to take Lawson's place in the 14-member squad.
Twenty-year-old wicket-keeper Carlton Baugh of Jamaica is due to make his Test debut in the same match to replace Ridley Jacobs, who is out of action with a torn muscle he suffered during the first Test in Guyana.
The West Indies suffered a crushing nine-wicket defeat in the first Test which ended on Sunday. The second Test starts at the Queen's Park Oval in Port of Spain on Saturday.
Brian Lara (captain), Ramnaresh Sarwan (vice-captain), Wavell Hinds, Devon Smith, Daren Ganga, Shivnarine Chanderpaul, Marlon Samuels, Carlton Baugh, David Bernard, Omari Banks, Vasbert Drakes, Mervyn Dillon, Pedro Collins, Tino Best.
