The defender joined Hearts earlier this week on loan for the next five games.
Dons chairman Dave Cormack confirmed Logan would then return to Pittodrie for the final few weeks of the season.
Logan’s contract runs out at Aberdeen prior to Brown joining as player-coach after the expiry of his Celtic deal.
The 33-year-old played down any animosity between the player following on-pitch run-ins and Brown's backing of Aleksandar Tonev.
The Bulgarian was banned by Scottish FA for racially abusing Logan during a Aberdeen-Celtic clash.
“On the pitch you have stuff with all sorts of players,” Logan told Sky Sports. “It's not that we didn't get on, he played for Celtic, I played for Aberdeen, there was rivalry on the pitch. He wanted to win, I wanted to win. I’ve had fights like that on the pitch for the last eight years, 12 years.
“I've not got a personal vendetta against Scott Brown, I don’t think he’s got one against me. Him coming to Aberdeen has nothing at all to do with me leaving. My contract's up.
"Am I his mate? No. Do I know him? No. Do I hear he is a good guy. Yeah. But I only judge people of what I've seen and come across. We've had a little bit of argry bargy on the pitch but, for me, it stays on the pitch.
“Anything else with other stuff people might be saying, him backing Tonev in the racism row, I've left all that in the past. It doesn’t bother me now. It’s so far gone I only ever think about it when someone brings it up. It has nothing to do with me leaving Aberdeen.”
Logan could be handed his Hearts debut this weekend when the Championship league leaders face Dunfermline Athletic at East End Park.
Neilson signed the right-back to provide more competition for the remainder of the season and the player assured fans he will give his all.
“I'll 100 per cent give Heart of Midlothian the same amount of effort I gave to Aberdeen,” he said on social media. “I know nothing else than to give 100 per cent.”