Q:

Merger of two or more political parties in U.S

Is there any process which allows merger of two or more political parties in U.S. if leaders of both parties are ready for a merger . Has such a thing ever occurred in history of US ?

A:

There is nothing that prevents it. The constitution allows for "free association". The right of parties to merge (or split) would seem to be constitutionally protected.
In the 1830s to the civil war, during the presidency of Andrew Jackson and the "Democratic Republicans" there were numerous parties that formed, merged, split: 
The National Republican Party and The Anti-Mason party merged to form the Whig Party, which then split on the issue of slavery. The parts reformed into the American Party and then with part of the Republican-Democrats, formed the Republican Party.
Later the People's Party, founded in 1891, formally merged with the Democratic Party in 1896.

