The duo have been brought in to add cover to the club's front line, which currently consists of first-choice pair Steve Torpey and Paul Hayes with Andy Parton in reserve.
Both are available for tomorrow's season opener against Rochdale.
18-year-old Irish striker Keogh is on the fringe of the first team at Leeds, and impressed with a goal for the first team against Darlington in pre-season.
He is described as quick and good with the ball at his feet, he takes shirt no. 27.
Bailey, who is also 18, has been given shirt no. 26 and United's official website bills him as a `giant striker`.
The two signings come after trialist striker Adrian Littlejohn rejected a short-term deal, and has now left the club.
Iron manager Brian Laws said: "I'm disappointed, I was willing to offer him a short-term deal to see how things go but he has demanded things I can't give.
"That to me is not the right way to do it because he is unemployed and I was willing to give him some employment. That is now the end of that."