Circa 1810 would probably be the outside limit. That's around when Beau Brummell, one of the King of England's closest friends and one of the most famous trend-setters of the 19th century --- people used to go hang out at his house in the morning for hours just to watch him get dressed --- led a shift from breeches and stockings to long pants with a cutaway coat, waist coat/vest, and neck cloth. The look is the basis for "white tie," which persists as the dress code for men at the most formal occasions. The biggest obvious difference would be the tie itself. In Brummel's day it was more of a scarf tied loosely around the throat, which evolved over the course of the 19th century into the modern bow tie (check the wiki pages of American presidents starting with Buchanan; he's got a cravat-style, but from Lincoln onward to moves gradually bow-tie-ward.)

Of course, you asked about business attire specifically. A modern business suit is somewhat less formal than white tie; the jacket has no tails and is cut evenly around the hem, pretty much. The shift from tailed coats to tail-less coasts for somewhat less formal occasions happened in the late 19th century, first becoming popularized in America among the wealthy members of a social club in Tuxedo Park, a suburb of New York City (thus, the tux). At a stretch you could go back to the early 19th century --- you'd be close but your jacket and tie would look weird --- but you could definitely blend in no problem by the 1890s, as long as you were wearing a bow tie.

Do you mean just a regular men's suit you might buy in a store today? Despite the perception that menswear never changes, there are in fact trends in men's tailoring. You would not be able to take a suit back more than about ten years before it started to look seriously out of place - though if you went back to the mid-1960s with a contemporary narrow-cut suit, you wouldn't be ridiculous at all - the narrow cut was stylish. But in, say, 1983, you would certainly provoke stares and comments because the fashionable suit had broad shoulders and wide lapels, hearkening back to the 1940s. There's no single cutoff point.

Would someone like to try and answer this question for women too? So every answer has ignored women's business attire/fashion.

1810 menswear is vastly different from modern business attire. The presence of cravats vs. the modern tie, the cut away style of frock coat vs. a modern suit jacket, trousers were effectively an entirely different beast in terms of fit and construction, a cultural expectation for proper headgear vs our modern preference to go hatless... A modern suit-wearing gentleman would stick out like a sore thumb in 1810.

The creation of the sack suit, which is the direct ancestor of the business suit, came about in the 1860s, but even then there are significant differences in fit and construction that would be fairly obvious even to an untrained eye. That said, it's the earliest I'd go with in terms of a style that would still read as a "suit" to both people in the 1860s and 2010s.

But it's really the nuances of fit and tailoring that are going to make it difficult for a time traveling businessman to blend in, even 20 years in the past. Our aesthetic is for sleek, tightly tailored jackets and flat-front trousers that fasten just above the hips. If you look at fashionable suits from the 1990s, you will see that the jackets were cut with less fitting to the torso and trousers were generally single or double pleated and buckled at the natural waist. The current 2010s silhouette shares more in common with the 1970s, believe it or not (just minus the obsession with polyester), so maybe you'd be able to blend in there, but go 10 years forward or back and you'd be back to sticking out like a sore thumb.