Why is 当然 the correct choice in 我学了10年汉语了，汉语水平 [一定 / 当然] 很高?
一定 either introduces an INFERENCE, which is very likely to be true (as in the context of the given sentence), or shows a strong intention (in other contexts). On the other hand, 当然, equivalent to the English 'of course', indicates an inevitable consequence that the speaker KNOWS to be true. 

In this sentence, since the speaker is talking about himself, he does not need to make an inference about him being good at Chinese; he knows he is good at Chinese. Therefore 当然 would make more sense here.

An easy way to differentiate the two is to translate the sentence into English with 一定 and 当然 replaced by 'must be' and 'of course', respectively, and you will be able to immediately see which one is better.