The England Under-21 became the Anfield club's first signing of what is anticipated to be a busy summer of transfer activity, and the Liverpool boss wasted no time in expressing his delight.
He said: "It is fantastic for the football club to be able to attract hugely talented young footballers that have huge potential.
"Jordan is very mature for his age. He is respectful and his principles and everything else on and off the pitch are exemplary.
"Not only is he a talented footballer, he's a really good person as well. He loves his football and he is very appreciative of what Sunderland have done for him.
Dalglish also claimed Henderson's capture is part of a longer-term plan at the club to boost performances.
He said: "You know of young players before of course but we have been watching him since he came into the Sunderland first team and have been tracking him.
"We just need to go out and bring people to the football club that will raise the profile and standard of the performances that we have had since January - and I think Jordan falls into that category. People might turn around and say, 'Well you have people in there who have done really well'.
"Of course they have done well - and hopefully next year people will be saying the same thing about Jordan."