Rovers had already brought central defender Ryan Edwards on a deal from Blackburn to give boss Ronnie Moore further options with Ash Taylor currently suspended and the 41-year-old Ian Goodison carrying a groin injury.
Moore continued to scour the market and clinched moves for Liverpool's Peterson, a 19-year-old who has been a regular fixture in the Barclays Premier League club's youth teams, and Otsemobor, a 30-year-old full-back from MK Dons, before Thursday's 5pm deadline.
Speaking to the club's official website, Moore said: "Kristoffer is a player I've had my eye on for a while.
"He's a fast, tricky winger who creates chances for others and has a good scoring record too."
On Otsemobor, who began his career with Liverpool and has a wealth of Football League experience having played for the likes of Norwich and Sheffield Wednesday, Moore added: "I'm really pleased to be able to sign Jon. He's an experienced player who can play right back, centre back or in midfield so he gives us plenty of options."