From the outside, you appear to be caught in a power struggle. Worse, it's one-sided; your new boss doesn't seem to realize (or believe) that your current boss is just trying to hold on to his existing team.
Quick aside - does your current boss have any reason to say anything like what he's saying? Have you left work 5 minutes early? Were you late for any meetings? Have you missed a deadline, even if it's just by an hour?
Anything concrete he can point to, no matter how small, is potential evidence he could bring up. Be sure that you're dotting your i's and crossing your t's the rest of your time under this boss.
If there is something, then you need to address that, with both your current boss and your new one.
To your current boss,
I understand you're not happy because I was late to the status meeting. Rest assured that it won't happen again while I'm still on this team.
To your new boss,
We were discussing John's comments about my lost motivation. I believe he was referring to a status meeting where I was late. I have already informed him that this won't occur again, and I wanted to let you know as well that I have every intention of staying productive during this interim period.
Absent any real evidence that you're "slacking off", I think your best bet is to schedule a quick meeting with your new boss. Let him know that you're unsure what your current boss could be referring to, but that you've noticed he isn't taking your departure very well, and seems to be frustrated that he has to find a new employee and get them up to speed. Assure him that you are still fully motivated, that you're excited to go to work for the new team, and that you'd never jeopardize your employment or reputation the way the current boss is accusing you of doing.
Ideally, you would follow up that meeting by having a meeting with the three of you to outline that:
a) you were completely within the company policy about the team transfer, and
b) you fully intend to fulfill your duties to the existing team throughout the three-month interim period, and
c) you don't want to be accused of any "slacking" that's not actually occurring.
Your boss needs to see that you recognize what's actually going on here, and that you're not going to accept slander without taking action to protect yourself. If your boss' boss could attend, he could make it clear that the transfer has been approved, and that he doesn't want to see any shenanigans in the meantime, but I'm unsure whether you or your new boss have enough influence to persuade him to attend.
Above all, your tone throughout this situation should be matter-of-fact - as though it's obvious what's happening, that you're simply informing everyone of what they should already know. You can't get angry, or upset, or vindictive; you have to continue to work with everyone involved after this situation clears up.
Ideally, your new boss walks away assured that you're committed to both your current and new teams, and the company as a whole, and your current boss understands that you're not going to put up with any additional rumor-mongering.