BBC reported on Saturday that the 29-year-old fast bowler is set to sign for the Welsh club for the rest of the season.
"We wanted someone playing here already and the West Indies squad was the first port of call," Glamorgan coach Adrian Shaw told BBC.
"He's slightly slower than Fidel Edwards, but still bowls at around 85 miles an hour and has got a much more solid action.
"He looks as though he'll stay fit and play a lot of cricket. He's a strong lad and a much improved bowler."
The club hopes to have Powell available for their first Pro40 match at Derbyshire on July, after he completes the West Indies' brief trip to Ireland for a series of three One-day Internationals against ICC Associate nations, the Netherlands on Tuesday, Scotland on Thursday, and the hosts on Saturday.
It will be Powell's first time in the County Championship, although he has played overseas for Gauteng in South Africa.
Powell snared four wickets for 40 runs from his allotment of 10 overs on Saturday to spur West Indies to a series-clinching, 93-run victory in the third ODI against England at Nottingham.