"It's been a pretty whirlwind few days," Mumford told media in Sydney on Thursday.
"When my contract talks were put off and put off again and then they signed Buddy, we started going hard at a couple of other clubs to see where I might be able to continue my career.
"I was lucky enough that the Giants could get me.
"As soon as we saw that (news about Franklin), we realised with the amount of money that he's going to be getting, there's probably not going to be anything there for me.
"So my manager started talking with GWS."
The Hawks were understood to be very keen to secure the 27-year-old's services, but the Bondi-based Mumford loves the Sydney lifestyle.
Accustomed to plenty of success during his time with the Swans and before that with Geelong, however, Mumford also knows he is facing a much different challenge with the young Giants.
"We were talking to Hawthorn as well, but how could I leave Sydney with weather like this?" he said.
"(I'm joining) a young club that's definitely going places.
"We have to embrace the challenge and with a few more experienced guys amongst the young kids there, there's a lot of talent there.
"We've seen that this year with guys like Jeremy Cameron that are going to be superstars of the game.
"With a few older and more experienced guys among that, I think finals is a possibility within the next few years for sure."
Mumford admits he was shocked by Franklin's mooted move to the Swans, saying "no one saw that one coming".
It also came as a surprise to the Giants, who had hoped to make Franklin their marquee signing.
But Mumford's decision is a significant step in the right direction for a team that won just one game in 2013.
The Giants are also believed to be chasing Collingwood's Heath Shaw, although AFL.com.au understands the Hawks and Cats are the frontrunners for his services.
Sam Fisher has also been linked with GWS, although a deal with the St Kilda defender is a long way from being completed.
Mumford is hoping his decision prompts some other free agents to follow suit.
"Someone had to be the first one and I don't mind being the first one off the rank," he said.
"The plan is obviously to get a few more experienced guys among the young group.
"It's just a bit of a wait-and-see for who they can talk to and get over the line."
Gemma Bastiani delves into stars of the 2024 Telstra AFLW Draft
10:57
The most spectacular marks of 2024
Relive the best marks of the 2024 Toyota AFL Premiership season
01:21
Why McDonald could become AFLW's best key forward
Gemma Bastiani delves into stars of the 2024 Telstra AFLW Draft
00:15
Opening Round QLD | March 6-9
Be part of AFL Opening Round to kick-off the 2025 Toyota AFL Premiership Season in QLD. March 6-9. Brisbane Lions host Geelong at the GABBA and Gold Coast SUNS take on Essendon at People First Stadium.