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It was a humble Lower East Side tenement where immigrants pulled themselves up by their bootstraps and into international prominence — and now it’s becoming a world-class destination of its own.

The Tenement Museum is putting the finishing touches on its new $13 million visitors center at 103 Orchard St., which will join the 20-year-old institution’s headquarters a few doors away.

The 123-year-old building, at the corner of Delancey Street, was at the heart of immigrant New York.

Once a German enclave, Yiddish-speaking immigrants began flooding Orchard Street in 1900. Lower East Side institutions like Ratner’s Delicatessen and Eldridge Textile Company teamed with a mostly Jewish clientele scooping up kosher food and stacks of socks.

Beginning in the 1920s, the ground floor of 103 Orchard became home to Zeiberg Hardware, crammed with nails and bolts of every sort and size.

The Zeibergs fled Russia in 1920, and they were so concerned about their safety that they melted down their gold coins and turned them into fabric-covered buttons. The store opened by the patriarch, Adolph, was a 24/7 family affair run by three generations.

“It was a daily grind,” said Marilyn Zeiberg, 74, whose future husband, Seymour, grew up working in his grandfather’s store.

Upstairs, Jewish immigrants jammed into tiny apartments. The corner building was home to 269 people living in 54 households, with four apartments per floor, according to the 1900 Census. There were two toilets to a floor.

In 1895, the Board of Health threatened to forcibly vacate the building for having unsanitary conditions.

“It was the most crowded place on earth,” said Allen Kurtz, whose in-laws, the Begechers, lived in the tenement from 1904 to 1910 after arriving from Romania.

The Tenement Museum will include information on what it was like living in the Lower East Side during the time period.

The Begechers worked in an uncle’s dry-goods store on Hester Street to pay off their passage to the New World. Other 103 Orchard St. residents toiled as tailors, cloak makers, butchers, peddlers and cigar makers, according to the 1900 Census. There was also one rabbi, a musician and a baker.

Given the conditions, Orchard Street dwellers busted their backs to get out.

Seymour Zeiberg studied engineering at City College, eventually becoming one of the nation’s foremost rocket scientists. He was deputy undersecretary of defense during the Carter administration.

The two-story tenement will open as new museum space on Sept. 20 and will nearly double the institution’s size to accommodate its 170,000 visitors a year.

The space — its last incarnation was a dress shop — will include a theater, gallery and classrooms for kids.