The award, voted on by the FWA's members, has been running since 1948 and crowns the player adjudged to have been the best of the season in English football.
Henderson said: "I'd like to say how appreciative I am of the support of those who voted for me and the Football Writers' Association in general. You only have to look at the past winners of it, a number of whom I've been blessed to play with here at Liverpool, like Stevie [Gerrard], Luis (Suarez) and Mo [Salah] to know how prestigious it is.
"But as grateful as I am I don't feel like I can accept this on my own. I don't feel like anything I've achieved this season or in fact during my whole career has been done on my own. I owe a lot to so many different people -- but none more so than my current teammates -- who have just been incredible and deserve this every bit as much as I do.
"We've only achieved what we've achieved because every single member of our squad has been brilliant. And not just in matches. Not just in producing the moments that make the headlines and the back pages but every day in training."
Liverpool boss Jurgen Klopp said: "I saw videos of him when he was young, but he was already an exceptional player. And you have to be ready to fight every day -- and that's what he's done.
"If you want to have a guy who has fought his way through to become one of the best players in the league and this year everybody acknowledged that. I am really proud of him."
Henderson beat stiff competition from Manchester City's Kevin De Bruyne after captaining Liverpool to their first league title in 30 years. He also played a key role in setting up the #PlayersTogether initiative, which helps raise and distribute money for Britain's National Health Service amid the coronavirus crisis. De Bruyne was runner up, Manchester United's Marcus Rashford was third while Henderson's Liverpool teammates Virgil van Dijk and Sadio Mane came fourth and fifth respectively.
The midfielder moved to Liverpool from Sunderland in 2011 and after his initial struggles, has gone on to establish himself as one of the club's key players.
Henderson won the Champions League with the club last season, as well as the FIFA Club World Cup and UEFA Super Cup in 2019-20.
"The players who've started the most games for us this season have been as good as they have been because of our culture and our environment at Melwood. No one individual is responsible for that -- it's a collective effort and that's how I view accepting this honour," he added.
"I accept it on behalf of this whole squad, because without them I'm not in a position to be receiving this honour. These lads have made me a better player -- a better leader and a better person.
"If anything I hope those who voted for me did so partly to recognise the entire team's contribution.
"Individual awards are nice and they are special and I will cherish this one. But an individual award without the collective achievement wouldn't mean anywhere as much to me -- if anything at all."