Dalglish is delighted by the deal and believes it's just rewards for a run of form that has seen Kuyt contribute seven goals since the Scot's return to Anfield as manager in January.
The boss told Liverpoolfc.tv at Melwood: "It's fantastic news.
"He's been a great servant to the club. He works tremendously hard, he's good in and around the dressing room, he's scored a few goals recently and his reward is an extension to his contract.
"He's delighted with it, and we're delighted for him and to have him.
"He's very good to have at the club, both on and off the pitch, and a great attribute for us.
"For us, the deal adds to the continuity of keeping people here that we want to keep.
"If he's happy then so are we."