Despite the Scottish transfer window ending on Saturday, Law and seven other new signings had to wait until Sunday to officially complete their moves to Rangers after a 12-month transfer embargo placed on the club officially ended.
And Law, who has scored four games in four matches whilst on trial at Ibrox, hopes he can now kick-start his career with the Glasgow giants.
"It is a relief," the 25-year-old told Sky Sports News.
"It has been tough, not just for us, but for the manager as well to pick his teams without eight of his new signings that he has brought in over the summer.
"It's been a strange situation but it's something we knew about really when we were signing for the club.
"We knew we wouldn't be registered for the first but we just got on with it."
Rangers have enjoyed a good start to life in Scottish League One, taking maximum points from their first four matches and cementing their position at the top of the league.
The former Motherwell midfielder believes McCoist may face a selection dilemma as he tries to integrate the club's new signings into the Rangers squad.
"We've worked hard and we've had a really good start to the season as well," said Law.
"So there will now be some tough choices for the manager I'm sure."