Got a new job!

I have been contracting off and on for the past 5 years, and I have just accepted a perm position. This contract was supposed to run out at the beginning of may, so I had 4 weeks left; technically I only have to give a 2 weeks notice, so I'm thinking I can start the new job in 3 weeks. The only problem is that the transition of my old job will be 'hey new guy, here's my stuff, bye!' so it kind of leaves them in a lurch as those last 2 weeks would have been my transition time.

Should I stress it or not? It really is only 2 weeks.