The Lions full-back from Wales started all three Tests against the Wallabies and with the series locked at 1-1 going into the final match; Halfpenny continued his fine form on tour by landing eight kicks in all.
Halfpenny kicked 21 points, a record for a Lion in a Test match, taking his own personal points tally for the three Tests to 49 points.
During the deciding game, which finished 41-16 to Warren Gatland's men, Halfpenny also set up a crucial try for George North which took the Lions clearly into the lead towards the end of the second half.
On receiving the award, Halfpenny said: "It's tremendous to be honoured and to receive this award but it was a true squad performance out here for us throughout the tour.
"It's been a long tour and to finish it off with a series win is a fantastic feeling. I am delighted I have contributed in such a talented and exciting Lions squad."
The award was presented to Halfpenny by Giles Morgan, Global Head of Sponsorship & Events for HSBC - the principal partner of the tour.
Morgan added: "Congratulations to Leigh on being voted the Player of the Series by all those in the media, thoroughly deserved recognition for an outstanding personal performance throughout the tour.
"HSBC is delighted to have played a part in what has been a hugely successful tour on and off the field for all those involved. It is particularly pleasing to end our second consecutive tour as principal partner of the Lions with a series win."
The British & Irish Lions leave Australia on Tuesday, heading back to Britain and Ireland with the Tom Richards trophy, the first time the Lions have beaten Australia since 1989.