Dale Pryde, 20, admitted climbing over fencing before running towards Mr Wallace at Hampden Park.
He also pled guilty to punching a Rangers fan and hitting another with a chair.
Pryde, of Greendykes, Edinburgh, was ordered to wear a tag for three months and carry out 250 hours of unpaid work.
Passing sentence at Glasgow Sheriff Court, sheriff Kenneth Hogg said he noted that Pryde was "deeply remorseful" although he said that his actions "merited the jail".
He added: "A footballer, no matter which team they play for, does not go on to a pitch to enable somebody at a later stage to run on and attempt to assault them - that's lunacy."
The court had heard how Pryde assaulted Jordan Gilmour by punching him on the head after the match that saw Hibs beat Rangers 3-2.
Pryde also admitted assaulting Megan Boyd by hitting her on the body with a chair during the same incident.
Defence lawyer Susan Walker said: "He's a Hibs supporter, he was overtaken by the occasion and behaved completely inappropriately. He completely accepts that."
She told the court Pryde drank too much and had "experimented with cocaine" at the time.
Ms Walker said: "He appears to have expressed genuine remorse and shame about his behaviour."
Thousands of Hibs fans jumped the barriers at the final whistle after their team won its first Scottish Cup Final in 114 years.
A number of Rangers fans also came on to the pitch.
More than 100 people have since been arrested and charged.
A Hibs fan who tried to punch Rangers player Lee Wallace during the pitch invasion that followed last year's Scottish Cup Final has avoided jail.