Glasgow Warriors head coach Townsend, 43, will take over from New Zealander Cotter in June.
The Warriors start their Pro12 season away to reigning champions Connacht on 3 September.
"We obviously want Scottish rugby to be a success and that starts with the national team and my own team, Glasgow," said Townsend.
"We've got the same goals. It'll be working on a similar way as before - how we manage the players, how we make sure that they're playing well for us and also playing well for Scotland."
Townsend goes into his fifth and final season in charge of Glasgow having reached the Pro12 final in two of the last three seasons, winning the tournament in 2015.
However, Warriors are yet to progress from the group stage of the European Rugby Champions Cup.
"Europe is the ultimate for any team that gets into that top 20, that get into the Champions Cup," said Townsend.
"With our pool - Racing, Leicester and Munster - it's going to be tough but that's the challenge we want to take on."
Ex-Clermont Auvergne coach Cotter will take charge of Scotland's autumn series against Australia, Argentina and Georgia before his final Six Nations as Scotland boss early next year.
And former Scotland fly-half Townsend, who previously worked with the national team as assistant to Andy Robinson, will take charge for the summer tour to Australia.
"That was a big pull, to coach nationally, that I would still be working with a group of Scottish players that I've really enjoyed working with," he said of his next post.
"I have really enjoyed and am enjoying being the Glasgow coach and I want to make the most of this next season with them."
Townsend was also asked if he would be available to assist the next Lions coach for their tour to New Zealand next year.
"My focus is firmly on Glasgow, a lot of work to do here," he added.
"There's been no conversations with anybody about the Lions.
"We're all waiting to see who the head coach is going to be. It's going to be exciting, as a supporter, just thinking about that tour and taking on New Zealand."
Scotland head coach in waiting Gregor Townsend says he and incumbent Vern Cotter have "the same goals" this term.