Question about credit and credit score?

My spouse and I have pretty bad credit right now. We owe almost 14k (all credit cards) and both have poor credit scores. However, we have come into some money and are planning on paying off all of our credit cards.

My question is this: How soon will our credit score improve? If we have everything paid off, will our score get bumped up automatically, or will we have to re-establish our credit with more credit (would like to avoid this if possible)? Once we are debt-free, we want to take out a mortgage, so this is a huge concern for us right now. Thanks.

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