The England U21 international, who is sure to feature for his country at the European Championships this summer, has scored 19 goals in all competitions since moving to the Riverside Stadium in August 2014.
His consistently strong performances have been vital to Middlesbrough's promotion push under Jose Mourinho's former assistant Aitor Karanka, with the club level on points with second-place Bournemouth following an impressive 1-0 win away to fellow promotion challengers Norwich on 17 April.
"Still can't believe it! Very emotional+proud night 4 me and my family. Big thanks to every1 at Boro, the club and the lads made it possible!" Bamford tweeted after collecting his award.
While the former Nottingham Forest trainee is evidently enjoying his latest loan spell, he will surely be hoping that his parent club and Mourinho in particular are keeping track of his rapid development.
Like several other of the club's stockpile of talented youngsters, Bamford has found his route to the first team blocked at Chelsea yet he could feature more prominently next season with the Premier League champions elect likely to bolster their strikeforce in order to provide cover for Diego Costa.
Costa is sidelined after suffering a recurrence of a long-standing hamstring injury during the 3-2 win over Hull last month and with chief back-up Loic Remy also nursing a calf problem, 37-year-old Didier Drogba was left as the only fit and available senior striker for the recent visit of Manchester United.
Reports that Chelsea are keen to open negotiations over a possible extension to Bamford's contract suggest he does figure in Mourinho's plans moving forward, although it would be wise for the player to seek assurances over playing time before extending his stay at Stamford Bridge.
Other winners at the 10th edition of the annual Football League awards included Kevin Phillips and Dele Alli, who scooped the Sir Tom Finney and Young Player of the Year gongs respectively.
Gareth Bale, Rickie Lambert and Adam Lallana were among the names featured in a special team of the decade and Bournemouth boss Eddie Howe was recognised for his fine work at Bournemouth.
Preston's Joe Garner enjoyed a memorable evening, winning the goal of the year award for his outstanding strike against Rotherham in last season's League One playoff semi-final and also being named as player of the year for the third tier.