The 30-year-old midfielder, who captained Liverpool to their first league title in 30 years this season, received more than a quarter of the votes.
“As grateful as I am I don’t feel like I can accept this on my own,” he said.
“I owe a lot to so many people but none more so than my current team-mates, who have been incredible and deserve this every bit as much as I do.”
Liverpool team-mates Virgil van Dijk and Sadio Mane, Manchester City’s Kevin de Bruyne and Manchester United’s Marcus Rashford also finished in the top five.
On Wednesday Henderson, who is recovering from a knee injury, received the Premier League trophy from Reds legend Sir Kenny Dalglish at a near-empty Anfield.
Henderson added: “I accept [the award] 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.
BREAKING: Jordan Henderson has been crowned the Football Writers' Association Footballer of the Year for the 2019/20 season.— Sky Sports News (@SkySportsNews) July 24, 2020
“If anything I hope those who voted for me did so partly to recognise the entire team’s contribution.”
Henderson also lifted the Fifa Club World Cup trophy for the first time in December.
Off the pitch, Henderson has helped raise money for the NHS as part of the #PlayersTogether initiative.
Arsenal and Netherlands striker Vivianne Miedema was named the Football Writers’ Association Women’s Footballer of Year. earlier this month.
– Guardian News