From a canonical point of view of TV shows and movies, the question as to who build the Sphere was not answered.
I do recall the Sphere being mentioned/used in Star Trek Online game detailing its history etc., but personally I hadn't played that part myself as of yet so I wouldn't know of the said details.
That said, Star Trek Online is NOT considered canon.
In regards to the novel that deals with the Sphere... well, again, the pocket books (including the technical manuals) are NOT considered canon.
But, the authors 'pet theory' which infers that the Borg's imperfect ancestors created it and then evolved into the Borg makes little sense.
For one thing, the Sphere's outer hull was made from Neutronium. Not even the Borg were able to create that material (which was said on screen by 7 of 9 - in Season 5 of Voyager, episode 'Think Thank).
You would think that if the Dyson Sphere was made from Neutronium by the ancestors who 'evolved' into Borg, it would be the choice of material used in construction of Borg ships and uni-complexes by default - which would make them impervious to all conventional weapons (unless of course the Federation improved phaser technology to the point it can incur damage to Neutronium, which you'd expect in the 100 odd years since they encountered the Planet Killer in TOS which used the same material and gave Starfleet plenty of time to analyze it in detail), however, the Borg on the shows (specifically in Voyager) were mentioned to be using Tritanium in their hulls (both regular and Tactical cubes) and relied heavily on nanoprobes and collective 'willpower/intelligence/energy' to repair and adapt their ships.
Janeway said that Starfleet theorized about making materials such as Neutronium but was not close in producing them... 7 of 9 answer to that was 'neither have the Borg'.
If Neutronium was difficult to produce due to resource shortages, that's one thing... not having an ability to produce it though is another matter.
Also, I doubt it would be impossible for the Borg to find needed resources in the Milky Way to produce enough Neutronium, especially with TW drives and highly advanced sensors.
No, from a canonical point of view, it does NOT appear that the Borg created it.
For all we know, the Sphere could have been created by the Iconians or another space-faring race.
In actuality, the Federation could have easily made its own Dyson Swarms around each Federation member world... although an actual sphere would not have been that much more difficult (and I disagree with Geordi's assessment that it wouldn't have been impossible - because the Federation technology is so far advanced that its not even funny), especially if each section of the sphere (made up of massive solar collectors) had fully integrated sensors, thrusters/impulse drives, transporters/replicators, etc. for self-replication).
In the real world, we could have already started and finished construction of our own Dyson Swarm by the year 2000 (if we started construction in 1990) using fully automated construction bots and Mercury for raw materials. Because construction would be automated, it would proceed on an exponential pace (something which scifi shows and many writers apparently have a difficulty showing/comprehending).
Anyway, point remains that we can only speculate on which species might have created the Dyson Sphere we saw in TNG.
There is no conclusive evidence on the subject matter.
The only thing that comes close (at least hypothetically) is the Planet Killer (which was made out of solid Neutronium much like the Sphere was). And it was mentioned that it likely originated outside of the Milky Way (possibly Andromeda).
It is possible that a species decided to come to the Milky way or has evolved in Milky Way, build the Dyson sphere, then left/evacuated to another galaxy and eventually built the Planet Killers too (who then found its way into Milky Way and started devouring planets during TOS).
Again, too little information.
Any number of species could have developed Neutronium as a material and built the sphere given enough time, or if they just used AI to radically accelerate R&D (something which the Federation could/should do).
TOS explained that the Kelvans migrated from the Andromeda Galaxy because it was experiencing a sudden increase in radiation which would have made their species extinct in 10 000 years.
They were also described to have been highly technologically advanced in comparison to the Federation of the 23rd century (probably/roughly on par with 24th century Federation given that the Enterprise-D was also stated in 'Where no one has gone before' by Data it would have taken just over 300 years to cross 2.7 million lightyears and get back to the Milky Way - putting at least their engine/Warp capabilities on par - which was of course completely discarded/forgotten by second season of TNG and later on by Voyager - or at least available/sustainable speeds were much lower than what was initially told).