Birmingham midfielder Charlee Adams has signed a new one-year contract with the club.
Southampton are confident Jay Rodriguez will commit to a new long-term deal but the player will consider his options.
The former Crystal Palace keeper looks set to return to London after a five-year spell with 1860, during which he made 168 appearances for the club.
Kiraly’s personal website reports Fulham, who were relegated from the Premier League last term, have paid a transfer fee in the region of £250,000 for the 90-cap Hungary international.
"I spent five years at 1860 Munich and it was a wonderful part of my life,” Kiraly told his official website.
"I got to know lots of people, I learned and experienced a lot here in Munich.
"I'll follow the happenings around 1860 Munich but this time I have decided to go back to Britain.”
Conversations with former Fulham players Zoltan Gera and Moritz Volz helped convince Kiraly to make the switch and the 38-year-old is relishing the prospect of joining Felix Magath’s side at Craven Cottage.
"I asked Zoltan Gera's and Moritz Volz's opinion who spent three and six years here,” he added.
"It's an honour to play for London's oldest club so I'll do my best to help the club to reach promotion.
"My whole family moves to London, my children will start the school here from September."
1860 sporting director Gerhard Poschner was quick to express his gratitude to Kiraly.
"We respect Gabor Kiraly so we accepted his wish to continue his career in England,” he said.
"He did his very best during his five years here and we thank him and wish him success at Fulham.”