The 21-year-old completed the switch from Celtic Park to Easter Road on Monday after it became clear his first-team chances under Ronny Deila would be limited.
McGeouch's only appearance of the campaign came in the much-changed line-up that fell to a 1-0 defeat by Inverness Caledonian Thistle. However, the Scotland under-21 cap is hoping to go from bit-part player to key performer.
"I went down to Coventry and things didn't really work out, but I'm looking forward to this move. I played a few games in pre-season with Celtic and got good fitness. I'm feeling fit and I just want to kick on now and, hopefully, get games for Hibs."