Gayle signed for Newcastle from Crystal Palace at the start of the month, and he has joined his new teammates in Ireland this week.
Newcastle are currently on tour, as Benitez puts his side through their paces ahead of the new campaign.
And Gayle said: "The training has been really good. We've seen a lot of the footballs, with keep-ball, possession drills and finishing. But there's also been a lot of shape and tactical work so it feels like we are covering everything.”
Gayle is expected to have an important role for Newcastle next term, with the striker one of a number of additions the Magpies have made so far this summer.
Newcastle have brought in five new players so far over the transfer window - with Benitez determined to improve the quality of his squad.
As well as Gayle, Newcastle have also brought in Matz Sels, Matt Ritchie, Isaac Hayden and Jesus Gamez.
Gayle could make his Newcastle debut at the weekend, when the Tynesiders play their first pre-season friendly against Bohemians.
The Magpies’ competitive campaign gets underway with a match against Fulham at Craven Cottage.