Rovers, who reached the final of the competition in 2000, will take on Forest at Prenton Park during the week commencing August 11.
"It think it's a really good draw," Edwards told the club's official website.
"They're one of the biggest teams in the Championship and, with a new manager, I think they'll fancy their chances of going up to the Premier League this season.
"So it's a tough tie for us, but one we will be up for and hopefully we'll get a big crowd at Prenton Park for it."
The two sides last met in the competition in the 2003/4 season, with Forest winning via penalty shoot-out after 120 goalless minutes.