My question is what will happen to these delegates? Will they be automatically assigned to Biden(because they endorsed him)? Or will there be another primary or caucus?
Short answer: No, the delegates that Buttigieg and Klobuchar are not necessarily assigned to Biden because they endorsed him.
Long answer: This a multi-layered issue which must be broken down by state rules, as well as a consideration of the upcoming primaries tomorrow (Super Tuesday). In the majority of states, those delegates from candidates who dropped out go to the national convention as "unpledged." At the DNC, these unpledged delegates seem to have a similar status as superdelegates, in that they can vote for anyone they chose.
However, there are certain states that insist those delegates must remain where they are (at least on the first ballot). Such states include Nevada and Virginia.
Of course, since Buttigieg and Klobuchar dropped out so recently, their names will appear on the ballots in the Super Tuesday states, so they might still accrue more delegates. (This might seem like a long shot, but we need to remember that early voting has drawn in big crowds this year.) Without having looked at each individual states' policy, I will assume that the Super Tuesday states have a mixed set of rules like the ones described above.
There might be more intricacies that I'm missing, but I hope this provides a general answer to your question.