Clyne has joined Saints from Crystal Palace.
Adkins said: "We're delighted we've brought Clyne into the group to help us kick onto the next level.
"There's a lot of work going on behind the scenes all summer and we work very hard to make things happen.
"For the last three years Clyne has been a very attack-minded full-back who bombs on, he's got pace and he's a good one-on-one defender.
"He got into the Championship Team of the Year last season and for such a young age he has had a lot of first-team football in the Championship.
"All being well, we can push him onto the next level now."