The fact he climbed out it is time. He can get really hurt and will continue to do it. I have always heard it doesn't matter what age, if they climb out time to get them out of the crib. Is it on the lowest level?
You can go get one of those zipper net things that goes over the top to keep him from escaping, those made me nervous.
First put his crib mattress on the floor, put him there and tell him not to get up.
I just got twin beds from my kids (toddler beds are a waste of money as they outgrow them so fast), but got bedrail for my son on his bed. After he turned 2 1/2 the bedrail came off.
I can say I had no real issue with them getting out of bed. They knew if I laid them down that was it and not to get back up somehow. Only now at their age do they come wake me up, hee hee. Also, make sure his room is dark at naptimes and bedtime, put a baby gate on his room doorway too.
There isn't a transition period when they have just climb out! Sorry.