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 ?
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.
It's certainly possible to merge political parties, as James K points out - it's happened many times. Really "merging" in most cases simply involves one party ceasing to operate, and the other continuing with some of the other party's membership - see for example, the Dixiecrats, who briefly formed from a group of Southern Democrats opposed to civil rights laws, failed to accomplish what they hoped in 1948, and then ceased operations after the 1948 presidential elections. Their members split, some rejoining the Democratic party for a while, others becoming independents, until the eventual swing of the South back to the Republican party.
In the case of non-major parties, the biggest factor here is ballot access. Most states have laws requiring parties to get a certain percentage of the vote in a general election, in order to have their candidate printed on the next year's ballot automatically (without requiring a certain number of signatures). As such, it is advantageous for smaller political parties to merge in order to be more likely to have easier ballot access. Further, starting a new party is very hard, given the difficulties of ballot access, but an easier way to get on the ballot is to find a small - but big enough - party that you can "merge" with.
Another significant factor is matching federal funds for Presidential candidates. Ross Perot (1992 and later) was interesting not just because he may have swung the 1992 vote (he may have, or may not have), but also because he managed to do well enough in 1996 to secure matching Federal funds in the amount of $12.5 million. Those funds are very significant for smaller parties, who don't have huge war chests to draw on. (Major party candidates generally do not accept them, as they come with lots of restrictions of what they can do in terms of fund-raising, but for third party candidates they're a huge sum.) Thus, if a few smaller parties were to begin to get sufficient votes that they might qualify for those funds, it would be unsurprising if they were to merge in order to qualify.
The most recent example is the Tea Party merging with the Republican Party.
One can, of course, argue whether the Tea Party was actually a party to begin with. Initially, most Tea Party members thought of it as an informal cluster of many groups with somewhat similar ideas.
Two reasons why I believe this merger qualifies for your question:
There is no formal definition of Party in the US in the first place. In the strictly legal sense, most parties are simply a group of related organizations (most of them non-profits), such as the RNC/DNC and others.
Nearly all the groups that made up the Tea Party were absorbed wholesale into the Republican Party at the same time. In that respect, they clearly acted as one unit, rather than many individual groups.
One other point: in no party is there a "leader" who could make such a decision. There are multiple high-ranking people who may together be able to make such a decision.
A second other, peripherally related, point: to some extent, the boundaries of parties is fluent to begin with. Quite a few members of one party ended up running on the ballot of another.
The most recent example is Bernie Sanders' Presidential run.
Another example, highly controversial to this day, is Joe Lieberman leaving the Democratic Party and forming his own, then running against the winner of the Democratic Primary (the Republican candidate in that Connecticut race was a nobody who got less than 10% of the votes), and eventually caucusing with the Democrats again.