Both players received an equal number of votes (34) for the A-League's highest honour, which were decided on by a panel made up of former professional players, technical experts, match officials and media representatives.
The two players just edged out last year's winner, Western United's Alessandro Diamanti, who received 31 votes. Melbourne City striker Jamie Maclaren (29) and Central Coast Mariners midfielder Oliver Bozanic (27) rounded out the top five.
Ninkovic, who has been with Sydney FC since 2015, becomes just the second foreign player to win multiple Johnny Warren medals following Thomas Broich, who won while playing for Brisbane Roar in 2011-12 and 2013-14.
The silky Serbia international won his first medal after a stand-out 2016-17 season with the Sky Blues, famously scoring the winning penalty in the 2017 A-League Grand Final to secure the club a third Championship.
His second medal this year comes after yet another impressive campaign as Sydney FC's midfield maestro, helping the club to their third consecutive Grand Final with four goals and four assists in 26 appearances.
Jointly awarded the medal alongside Ninkovic is Davila. After signing with Phoenix in 2019, the sizzling attacking midfielder was crucial in leading the club to their best-ever regular season finish (third) in 2019-20 with 12 goals and five assists.
While the Nix just missed out on finals this season, Davila was none the less a key player for the club, scoring seven goals and assisting seven more as the club finished seventh by a single point.
Heyman, who received 19 votes, just edged out Brisbane Roar's Emily Gielnik and Melbourne Victory's Kyra Cooney-Cross, who each received 17 votes. Sydney FC's Cortnee Vine and Adelaide United's Emily Condon both finished with 12 votes, making up the top five.
Like Ninkovic, Heyman also becomes one of a handful of players in Australian football history to win the medal multiple times. She was last awarded the league's top honour in 2009 and now joins Sam Kerr, Clare Polkinghorne, and Taryn Rockall with two Julie Dolans each.
Heyman's win comes after an incredible comeback season, returning to Canberra United after almost stepping away from the game altogether. The veteran Matilda was a key figure in the club's return to the top four, scoring 10 goals and assisting three in 12 appearances.
Despite missing out on the Julie Dolan Medal, Victory's Grand Final goal-scorer Cooney-Cross was awarded the W-League's Young Footballer of the Year, while Sydney FC's Joel King took out the A-League equivalent.
Melbourne City's Patrick Kisnorbo was named A-League Coach of the Year after winning the Premiers Plate and guiding the club to the 2020-21 Grand Final in his first season. Melbourne Victory's Jeff Hopkins won the W-League Coach of the Year for the third time in his career after the club's sensational Grand Final win over Sydney FC back in April.
Melbourne City striker Maclaren won the A-League Golden Boot award with a record-breaking 25 goals, while Brisbane Roar's Gielnik took out the W-League Golden Boot with 13.
Between the sticks, the A-League Goalkeeper of the Year was jointly-awarded to Sydney FC's Andrew Redmayne and Central Coast Mariners' Mark Birighitti, while Melbourne City's Teagan Micah won the W-League award.
Perth Glory's Andy Keogh scored the A-League Goal of the Year after his long-range strike against Western Sydney Wanderers in round 21. Melbourne Victory winger Lisa De Vanna's solo slalom effort in the Melbourne Derby in round 3 was the W-League's Goal of the Year.
Elsewhere, Brisbane Roar won the Fair Play awards in both leagues after accumulating the fewest yellow and red card points, while two of those responsible for handing them out -- A-League referee Chris Beath and W-League referee Rebecca Durcau -- were each named Referee of the Year in their respective competitions.