The Hartlepool striker initially joined the Dens Park side until January but both clubs have agreed an extension to the loan deal.
Nish has netted twice so far this season and is determined to find the goals in the second half of the campaign that could help the Dark Blues retain their top-flight status.
"It's been confirmed now that I'm staying so I'm happy with that," he said.
"I was hopeful of staying, that was my preferred option. It was down to the two clubs to sort out and it has happened now so I'm delighted.
"I just need to try to get some goals and some points on the board now."
A 1-0 defeat to St Johnstone on Wednesday left rock-bottom Dundee nine points adrift of nearest rivals Ross County heading into the winter break.
Nish said: "It was a poor game. We weren't dangerous going forward and neither were they - it was just a poor game.
"We didn't look like scoring at all and I don't know why that is. It's just pretty disappointing."
However, the forward still has belief in Dundee's ability to forge a run of results between now and the end of the season.
He added: "We know we can do it but we need to do it, rather than just saying it. We need to start winning games. It's simple."
A report claimed the Dens board are set to discuss boss Barry Smith's future, while a banner at half-time at McDiarmid Park read: "Smith must go."
Nish can understand the frustration of the supporters but insists everyone must pull together.
He said: "The fans have been brilliant all season. Even when we've been getting beat they have been brilliant.
"They have stuck by us, even though we haven't been getting results lately.
"It will be hard for them to take, the same as it is for us.
"We need them to stick by us. As a team and as a club we need everything going in the one direction.
"It is difficult. We are gutted after this game and we seem to be gutted quite a lot recently. Things just don't seem to be going right but we just have to keep working hard."
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