The club said they are 'disappointed' after learning of the outcome. It is not yet known what the pair have been charged for.
The Blades say both Brewster McBurnie 'strenuously deny the charges' after attending voluntary interview with Nottinghamshire Police.
The fixture that took place on May 17 saw a pitch invasion at the end of the game by jubilant Nottingham Forest fans, leading to an assault on Sheffield United striker Billy Sharp.
Sharp needed stitches after falling victim to a vicious attack by Forest season ticket holder Robert Biggs.
Biggs was later jailed for 24 weeks after pleading guilty to assault occasioning actual bodily harm.
A statement from the Blades read: "Sheffield United Football Club is disappointed to learn that Rhian Brewster and Oli McBurnie have been charged following the incidents that took place at the EFL Championship play-off semi-final second leg against Nottingham Forest last month.
"Both players voluntarily engaged in interviews with Nottinghamshire Police in the aftermath of the fixture which saw their team-mate, Billy Sharp, the victim of assault in the chaos which followed the final whistle.
"Brewster and McBurnie strenuously deny the charges brought against them and football manager Paul Heckingbottom, who wrote letters to the League Managers' Association, the Professional Footballers' Association, the EFL and FA following a number of pitch invasions last month, including one involving Crystal Palace manager Patrick Vieira, is continuing discussions with key stakeholders in a bid to better protect players and staff in their place of work."
Sheffield United clawed back a two-goal first-leg deficit to level the tie at 3-3 on aggregate, forcing extra-time and penalties.
But Forest had goalkeeper Brice Samba to thank as he saved three spot kicks to send Forest to Wembley where they eventually sealed their return to the Premier League as they overcame Huddersfield Town.