The 26-year-old came through the youth ranks at Bramall Lane, before leaving them for the Iron in 2007.
He joins on loan until the end of the season from Southampton.
Meanwhile 34-year-old Robson is a free agent after leaving Major League Soccer side Vancouver Whitecaps this month.
"People will be familiar with Jonathan's talents and we are delighted that he has accepted our offer to come and play," said Sheffield United manager Danny Wilson.
"His goalscoring record is very good and hopefully he can improve that back in Sheffield with us - he is undoubtedly a player with great potential."