Old blog, new blog, search engines

I have an older free blog on wordpress, but recently moved to my own host. I exported/imported all the old posts from the old to the new. I put up a static “I moved” page at the old blog and deleted posts in the old one as well.
However, when I type keywords into Google, it refers to my old blog rather than the new and clicking on the link shows my old website with a “Ooops…where did you get such a link?” post.
Why does a keyword prefer my old site over the new? How do I ensure that traffic goes to my new site? I’d like to keep the old blog in place for awhile to direct people to the new site, but I want keyword traffic to go to the new.
thanks
Melody