McGeouch, a 21-year-old Scotland Under-21 international, previously enjoyed a loan spell at Coventry City last season while Sinclair, 19, is a graduate of the Saints successful youth academy.
After completing his move to the Scottish Championship side, McGeouch said: “I’m really excited.
“Hibs are a massive club and as soon as I became aware of the interest I wanted to move to Easter Road.
“My aim is to play as many first team games as possible and help to get the club back where it belongs; in the top division.”
Sinclair, younger brother of Manchester City winger Scott, said: “I’m really impressed by everything at the club and it’s great to be here – now I can’t wait to get started.
“My under-21s coach at Southampton told me about the possibility about moving to Hibs on loan on Friday and, as soon as I heard about it, I jumped at the chance.”
Meanwhile Hibs boss Alan Stubbs said: “They will offer us something different and strengthen our attacking options.
“Dylan comes to us with a high reputation earned at Celtic and we see him playing in a more central role in midfield.
“Jake will give us a few options in attack; through the middle and out wide. He is a really exciting player with genuine pace, who can hurt the opposition.”