"We are working hard, and the boys have also been working hard and showing that they are enjoying training," the Englishman said on Thursday.
Baxter, who coached Bafana Bafana between 2004 and 2005, officially took over the coaching position a month ago.
The relationship between the majority of the squad players and his predecessor, Vladimir Vermezovic, had reached a low last season, leading to his sacking before the end of the season.
Amakhosi failed to win any silverware last season – a rare situation for the country's most successful club.
Players had been vocal in wanting a coach who would not restrict their freedom on the pitch, and had better man-management skills.
"The one challenge as a European coach is that players in Europe like detailed and structured methods," Baxter said.
"African players want something more spontaneous and challenging … I want the boys to have both, the European effectiveness and at the same time, be able to show their flair."
Baxter's first assignment in the hot seat is this Saturday's pre-season Gauteng Cup tournament in Atteridgeville.
Chiefs face Moroka Swallows in the second match of the day. Should they win they will play the winner of the earlier fixture, between Wits and SuperSport United, in the final.
Baxter is likely to debut new recruits Morgan Gould and Eric Mathoho, as his centre-back pairing, and include Siyabonga Nkosi in midfield.
Gould could be a crucial ingredient in the Chiefs backline this season, with his strong presence and leadership qualities, aiding captain and goalkeeper, Itumeleng Khune.
Nkosi will compete against Reneilwe Letsholonyane and Lucky Baloyi for a berth in the middle of the park.
Up front, former Black Leopards goal poacher Kingston Nkhatha may also be given a chance on the weekend, despite carrying a niggling foot injury.
"Morgan has been professional and adapted well, and Tower [Mathoho] is getting there as well," said Baxter.
"Nkhatha as well has started to relax a bit, and is looking to be imposing … He'll be all right for the weekend, and may get some time to play." – Sapa