Postecoglou has been named Manager of the Year for the second successive season after leading the Hoops to back-to-back titles, with a 2-0 win over Hearts on May 7 clinching top spot with four games to spare.
The Australian boss has become the first-ever Premiership manager to win the award in consecutive years and just the second manager after Gordan Strachan (2006-07 and 2008-09) to claim the award twice.
Celtic, who also won the Scottish League Cup earlier this year, remain on course to win the domestic treble, with a Scottish Cup final against Inverness Caledonian Thistle to look forward to at Hampden Park on June 3.
Japanese forward Furuhashi has received the Player of the Year award having enjoyed another excellent campaign in front of goal, scoring a league-high 24 goals in 32 league games so far this season.
The 28-year-old, who netted his 50th goal for Celtic in the title-clinching victory away against Hearts, fended off competition from last year's winner and teammate Callum McGregor, Reo Hatate and Motherwell's Kevin Van Veen to become the first Asian player since Shunsuke Nakamura (2006-07) to win the award.
Meanwhile, Celtic winger Jota received the Goal of the Season award for his brilliant chip against Old Firm rivals Rangers in September.
The Portuguese, who has netted 11 Premiership goals in 31 appearances this season, ran onto a pass from Matt O'Riley before lifting a sweet chip over Allan McGregor from a tight angle, scoring the second goal in a thumping 4-0 home victory over the Gers.
Elsewhere, Rangers midfielder Malik Tillman - on loan from Bayern Munich - scooped the Young Player of the Year award having enjoyed an impressive first season in Scotland, contributing with 10 goals and four assists in 28 league matches.
The 20-year-old American beat Celtic duo O'Riley and Liel Abada - last year's winner - and Albion Rovers' Charlie Reilly to become the first Rangers player since Ryan Kent (2018-19) to win the award.
In the lower divisions of Scotland, Ayr United striker Dipo Akinyemi won the Championship Player of the Year award, while Airdrieonians' Calum Gallagher and Albion Rovers' Reilly collected the top awards in League One and League Two respectively.
Former Aberdeen and Manchester United manager Sir Alex Ferguson, meanwhile, received the Special Merit award in the same week marking the 40th anniversary of the Dons' European Cup Winners' Cup triumph under the legendary Scotsman.