I had two interviews with prospective company. I signed an offer letter and W/9 pending background and drug screen.
I took my drug screen and I know all will be good. Problem is background check will show a DUI in 5/09 and 02/10.
On put that information on the application the same day I signed the offer letter. What are my odds I will get the job?

No one can give you odds on this. Best bet is to make a follow up call to the company to see what the status is. My recommendation would be to NOT mention the DUIs, but to simply say "I am following up on the status of the position that was offered me"... and see where it goes from there.

It really all depends on who else was interviewed. If there are others with same or better qualifications but no criminal record, they will most likely be hired.

If the job involves driving for the company, even errands, you may find difficulty. Sorry to say but most insurance companies will not cover a driver with 2 DUI's in 3 years.

Did you include these arrests on your application? Were you asked about it?

The asker did say that s/he did disclose the previous DUI offenses.

I was asked on application and I did disclose it. The position does not involve driving.