The 27-year-old Welshman, who arrived in late March, scored 32 points in the last four Pro 12 games.
Tovey said: "Having the opportunity to come up to Edinburgh and play some rugby was definitely the right move for me and I'm loving it here.
"I couldn't have asked for more from the boys over the last six weeks."
After a winning debut against Zebre, Tovey was unable to prevent Edinburgh slipping to defeat in their final three matches against Munster, Leinster and Cardiff Blues to finish ninth, one place lower than the last two seasons.
Head coach Alan Solomons has instilled a structured style of rugby in the capital, spearheaded by a fearsome pack, a robust set-piece and a strong defence but without a great deal of attacking flair.
Edinburgh only managed to claim a try bonus-point - for scoring four or more in a game - twice this season, crossing the whitewash on a total of 41 occasions.
"That's something we've got to look to bring into our game and start scoring a lot more tries," Tovey said.
"I think the last couple of weeks of the season we tried to change a bit, tried to play a different brand of rugby.
"But there's certain times where we've got to go back to that style and use our big heavy pack and I'm sure pre-season will come and we'll try and mix it up a bit more.
"That comes down to nine and 10 - they're the ones controlling it."
Tovey will compete for the number 10 jersey with Scotland fly-half Duncan Weir, who is joining from Glasgow Warriors.
Weir could be absent for chunks of the season on international duty and there is likely to be a preference in the Scotland camp for the native man to start.
However, Tovey says he's comfortable playing at full-back if required but will face competition there from impressive youngster Blair Kinghorn and Glenn Bryce, another new signing from Glasgow.
"He's a Scottish international, so it's always nice to have two 10s," Tovey said of Weir. "Hopefully both playing well at the same time, creating competition and getting the best out of each other.
"I'm not too sure about playing 12. I started off my career at full-back, so there'd be no dramas there, but Blair Kinghorn this season's been great and we've got Glenn Bryce coming in as well - two quality full-backs."
Fly-half Jason Tovey has signed a two-year contract with Edinburgh until May 2018 after a loan spell from Newport Gwent Dragons.