The pop group were supposed to play Manchester Arena this weekend, but those three shows were scrapped after the attack that killed 22 people.
They will now play a single date at the Etihad Stadium on 18 June instead.
Appearing on stage in Liverpool on Friday, Howard Donald spoke of his pride in "the spirit of Manchester".
Bandmate Mark Owen dedicated the concert to "everyone who has been affected by the events that happened in Manchester last Monday night".
He added: "All profits from tonight will be going to We Love Manchester emergency fund."
The fund was set up by Manchester City Council and the British Red Cross to raise money for those who were bereaved or injured as a result of the attack on the Ariana Grande concert at the arena.
It has raised more than £5m so far, with former Oasis frontman Liam Gallagher and rapper Eminem among the other music stars to have pledged money.
Take That's show at Liverpool's Echo Arena was originally scheduled for Tuesday, but was postponed to Friday by the band "out of respect" for the victims and their families.
On stage, the band paused after the first song to give their response to the week's events.
Howard Donald said: "As you know, I was born and raised in Manchester, so at this moment in time, I've never been so proud to be a Mancunian.
"Thank you so much, thanks for coming and enjoy the night please."
Gary Barlow said: "Obviously ladies and gentlemen this is going to be an emotional night for us all.
"We should have been playing Manchester tonight as you all know. We want to say an enormous, enormous thank you to all you guys out there who have come back, I know we were meant to here on Tuesday thank you so much for coming out tonight."
Earlier, the group announced that they will play at Manchester City's stadium next month instead of rescheduling this weekend's three Manchester Arena shows.
Fans with tickets for the postponed arena gigs can choose to exchange them for the Etihad date or get a full refund.
Meanwhile, Ariana Grande has promised that she will return to the "incredibly brave city" to stage a benefit concert.
And a number of other announcements have been made about Manchester Arena events and other concerts in the city in the wake of the attack:
No details have been given about when Manchester Arena will reopen. The next event in the venue's diary is a Kings of Leon concert on 9 June.
Take That have paid tribute to their home city of Manchester, pledging to give the profits from their first show since Monday's bombing to charity.