Kopitar and Žolnir were selected as the nation's best male and female athletes by Slovenian sports writers in a vote held in December by the Sports' Writers Association of Slovenia (DŠNS).
The pair were conferred the awards at a ceremony held annually by the DŠNS to honour Slovenia's top sporting achievers in the past year.
The 25-year-old Kopitar, who was a key member of the Stanley Cup-winning Los Angeles Kings outfit earlier in the year, beat out hammer thrower Primož Kozmus, a silver medalist at the London Olympics, in the voting 261 to 182 to become the first ever athlete in a team sport to win the award.
Shooter Rajmond Debevec, who won bronze in London, came in third with 55 votes.
Like for Kopitar, this is also the first Athlete of the Year honours for the 31-year-old Žolnir, who tallied 344 votes from the sports writers.
The judoka, who was close to retirement three years ago after undergoing operations to both her knees only to come back in style in London, finished ahead of three-time winner, skier Tina Maze (286) and climber Mina Markovič (72).
Meanwhile, rowing duo Iztok Čop and Luka Špik, who won bronze in the double sculls in London, were awarded for the Best Team of the Year.
The DŠNS also conferred a special award to paralympic shooter Franček Gorazd Tiršek, who took silver in the London Games.