Idiom / expression for someone who forgets their roots on achieving success

One such is nouveau riche:

noun [treated as plural] (usually the nouveau riche)

people who have recently acquired wealth, typically those perceived as ostentatious or lacking in good taste

[ODO]

[A rolling stone gathers no moss is not the same]

"A rolling stone gathers no moss" is a proverb rather than an idiom. It means that people who constantly move from one place to the next never make money or friends.

A proverb that meets your definition is:

Set a beggar on horseback, and he'll ride to the Devil.

(Source: Proverb Hunter)

Consider social climber

a person who strives to gain a higher rank in society, usu. by associating with more socially prominent people.

Social climber is a term that could be used by someone of any social status when characterizing a person seeking to be accepted in a status higher than previously inhabited.

You might also consider

• arriviste
• parvenu
• upstart

These last three are more likely to be used by someone of a higher class looking down on the climber. The last may have special issues in its use (at least in the US) because of its association with the term uppity

putting on or marked by airs of superiority : arrogant, presumptuous

This term was used extensively in the 20th century to refer negatively to African Americans (and sometimes other minority groups) who sought to be treated equally.

Such a person is often described as "Putting on airs."

A single-word that describes this is "pretentious." It implies that the person is undeserving of of their current position.

Other synonyms include poseur, poser, and imposter.

The best I can come up to describe the sentiment: Power corrupts. Absolute power corrupts absolutely.

If you wanted, you could put your own spin on the phrase: absolute wealth corrupts absolutely.

After two days I think I have it: victim of one's own success.

Such a person can be said to have "forgot where he came from", meaning he's forgotten his humble roots and is acting as if he was born to wealth.

Perhaps not the best answer, but a related (and useful) quote:

It pays to be nice to the people you meet on the way up, for they are the same people you meet on the way down. — Walter Winchell

There's also the more ghetto-type phrase (relevant, although vulgar):

Acting like your [excrement] doesn't stink.

"Forgetting that the rungs on the ladder to success are people, not things to be stepped on."

In other words, people provide us with the rungs on which to climb the ladder of success; they themselves are not the rungs to be stepped on on the way up!

I generally hear this (sad to say) in racial terms.

For instance, a black person who does this is called an "Oreo" (black on the outside, white on the inside). A Native American in this situation is called an "Apple". (red on the outside...well, you get the idea). I've heard of Chinese similarly being called "bananas", but I'm not acquainted with enough Chinese to know how common that one is.

kick away the ladder

burn the bridges

American Midwesternism:

"Dropped his past like a live grenade." Sometimes "dropped his friends like a live grenade" or "dropped the old neighborhood like a live grenade."

Point of the metaphor is that he didn't just quietly stop having anything to do with where he came from; he treated like something dangerous (the way a live grenade is). To drop is just to pretend it's not there; to "drop like a live grenade" is to take active measures to get it away from you.

"Boy, don't he think he's walking in tall cotton!" --Something my grandad says about people who are suddenly too good to pay you any mind.

wake up one day thinking the sun shines out of one's ass

think the sun shines out of (someone's) backside/butt/ass/arse (chiefly BrEng)

To believe a person is better or more important than others or above reproach. (Note: If thought about oneself, it means that they are arrogant, conceited, or self-absorbed. If someone thinks this of another person, it means that he or she loves or admires that person to such a degree as to be blind to any of their potential faults.) Tom has acted like he's such a hotshot after getting the promotion. He thinks the sun shines out his backside! He's absolutely head-over-heels in love with Mary. Even though I find her a bit irritating, he thinks the sun shines out her backside.

Farlex Dictionary of Idioms

forget the hand that fed you

Google Books

bite the hand that feeds (one)

To repay generosity or kindness with ingratitude and injury.

American Heritage® Dictionary of the English Language

You might say that such a person has gotten too big for his/her britches or gotten too big for his/her boots:

Conceited, self-important, as in Ever since he won that tournament he's gotten too big for his britches, or There's no talking to Jill anymore—she's just too big for her boots. This metaphoric idiom alludes to becoming so “swollen” with conceit that one's pants or boots no longer fit. [Late 1800s]

(http://www.dictionary.com/browse/too-big-for-one-s-britches)

By itself it doesn't necessarily imply that someone came from humble beginnings, but used with "gotten" it suggests a change in someone's behavior.

We have a bengali saying to describe such a person. When translated to English it goes something like this: When you drop a fish from the small pond into the big pond, it dances around in wild excitement.