The adjective swellegant means wonderfully stylish, elegant or fashionable.

Of American-English origin, this adjective is a blend of swell and elegant.

Before the adjective swellegant came into use, the adjectives swell and elegant were sometimes used in juxtaposition. The earliest occurrence of swell elegant that I have found is from an advertisement for Wakefield & Lee, published in The Morning news (Savannah, Georgia) of Sunday 5^th March 1893:

FOR SPRING
YOU WANT THE PROPER “SWELL ELEGANT,” SO DON’T FAIL TO SEE
WAKEFIELD & LEE,
THE HATTERS, HABERDASHERS AND SHOE MEN,
27 BULL STREET REAR THEUS BROS.’

This gave rise to the compound swell-elegant (sometimes swellelegant – cf. quotation 4 below). The earliest occurrence that I have found is from the following advertisement for Stern & Bendheim, Altoona, published in the Morning Tribune (Altoona, Pennsylvania) of Monday 2^nd February 1903:

Satisfactory Swap
A Howard Hat
And Nothing to Boot

Just three common, ordinary United States dollars will get one of these swell-elegant, Spring style hats—just as good as any hat that ever brought $5.00 with another label—and we ask no boot.
The splendid quality, the advance style, the big assortment of attractive shapes and new colors—all thrown in free. You only pay what you would have to pay for an ordinary hat, $3.

These are, in chronological order, the earliest occurrences of the adjective swellegant that I have found:

1-: From Upper Iberville Notes, published in The Weekly Iberville South (Plaquemine, Louisiana) of Saturday 9^th November 1901:

For the benefit of the public school here a ball was given in the new public school building on Sunday night last. […] We sent down and secured a baby baboon band from Plaquemine, and at half past seven began to whirl around the spacious school room with our sweet dimpled-cheeked maidens as we gracefully indulged in a waltz to the sweet strains of the swell’egant music.

2-: From Local News, published in the Warren Sheaf (Warren, Minnesota) of Thursday 6^th February 1908:

An orchestra, consisting of Oscar and Joseph Hilden and M. Solum, of Oslo; M. Coucheron, of Adams, N. D.; Gust Jull and Chas. Grinder, of this city, furnished music at a dance given at the opera house on Friday evening. It is needless to state that the music was “swellegant” and it is hoped that they will furnish music a more dances in this city in the near future.

3-: From The Daily Telegram (Long Beach, California) of Tuesday 7^th April 1908:

A scene of rare beauty will the north one-half of the Hotel Virginia diningroom be found tonight when the three-hundred banquetters march in to enjoy the swellest and most elaborate annual banquet ever given under the auspices of the Chamber of Commerce. […]
[…]
The menu will be “swellegant,” and the speeches which will follow will provide the most entertaining and instructive program of wit and wisdom which has ever followed after a banquet served here.

4-: From the Springfield Daily Republican (Springfield, Massachusetts) of Tuesday 23^rd September 1913:

Peculiarities of Speech of the Yankee and Westerner to Be Preserved.
[Perry W. Long in the Boston Transcript.]

With a view to preparing ultimately a dialect dictionary, corresponding in a measure to the English dialect dictionary, the American dialect society is storing up information regarding Yankeeisms, Americanisms and curious pronunciations and locutions. […]
[…]
[…] To note one feature, the tendency to invent all manner of contaminations in the expression of pleasure or admiration appears to be very widespread in the United States. In a study—which might better be termed recreation—dealing with terms of approbation and eulogy, Miss Elsie L. Warnock of the university of Nebraska records a phantasmagoria of terms—largely drawn from schoolgirl speech—which remind the reader of “Alice in Wonderland.”
To quote briefly: “How do you like that candy?” “It’s just expollagollucious.” “This pie is lobdocious.” “That’s superglobsloptious pudding.” Surely the gourmand here may be said to chortle in his joy. Among other terms several from Nebraska which denote an exceptionally stylish person or thing are: Dinger, humdinger, lallapaloosa and peachamaroot. One only fears that they are not confined to Nebraska, that, rather, they are no less omnipresently dear to the heart of the school miss and matinee girl than are the equivalent adjectives, swelldoodle, scrumdoodle and skwuzzy. The school miss especially delights in combining and contaminating her pet expressions. Swellelegant and swellegant are cases in point. Perhaps one of the oddest of such terms for a stylish person is the western term, gogetter.

The adjective swellegant was popularised by its use in the song Well, Did You Evah! ¹, interpreted by Bing Crosby ² and Frank Sinatra ³ in the 1956 film High Society:

Have you heard, it’s in the stars
Next July we collide with Mars
Well, did you evah
What a swell party
A swell party
A swellegant, elegant party this is.

¹ Well, Did You Evah! was written by the U.S. composer and songwriter Cole Porter (1891-1964) for the 1939 theatrical musical Du Barry Was a Lady.
² Bing Crosby (Harry Lillis Crosby – 1903-1977) was a U.S. singer and actor.
³ Frank Sinatra (Francis Albert Sinatra – 1915-1998) was a U.S. singer and actor.