Which of the following sentences is correct?
He as well as they are in the wrong.
He as well as they is in the wrong.
Sometimes the expression "as well as" behaves like the coordinator and, and sometimes it doesn't.
In your example(s)--and because delimiting commas aren't used--perhaps the preferred interpretation could be that the expression "as well as" is behaving as the coordinator and. And so, perhaps your version #1 could be the more natural one:
- He as well as they are in the wrong.
Here, the plural verb "are" agrees in number to the notional plural subject. Compare to "He as well as she are in the wrong", "Tom as well as Sue are in the wrong".
A decent usage dictionary will usually have info related to this topic. For instance, in my copy of the Merriam-Webster's Concise Dictionary of English Usage, it has the entry "as well as" on pages 101-2, where it discusses the coordinator usage of that expression.
For related info from a vetted grammar source, there's the 2002 CGEL, pages 1316-7:
As well as
. . . There is also an idiomatic use meaning approximately "and, in addition to", illustrated in:
i. a. She [means what she says] [as well as says what she means].
i. b. [Abstraction] [as well as impressionism] were Russian inventions.
i. c. [Both increasing ewe liveweight,] [as well as liveweight at mating,] influence ovulation rate and lambing performance.
. . .
In [i] as well as behaves like the coordinator and. In [i.a] it links two finite VPs, a property characteristic of coordinators: cf. property (c) of &2.1. . . .
In [i.b] the form were indicates that the subject NP is plural, just like abstraction and impressionism.
And in [i.c] we have not only such plural agreement, but also a correlative pairing of both with as well as instead of the usual and.
In CGEL, there are also examples of singular verb usage, e.g. [70.ii.a] "Beauty as well as love is redemptive."
In conclusion, the answer probably comes down to whichever version you prefer, which could come down to the context, and/or the style guide of the publisher.
Note that CGEL is the 2002 reference grammar by Huddleston and Pullum et al., The Cambridge Grammar of the English Language (CGEL).