The former Liverpool player cost Tottenham £2m when he signed from Charlton in January 2006.
Kuqi has come in on loan until January to help fill the void left by Brian McBride, who has a dislocated kneecap.
Sanchez told the club's website: "Danny Murphy is a proven England international player with great vision, experience and ability.
"He can split the defence with a single pass and can score goals so I'm delighted he's chosen to come to Fulham at this stage in his career.
"It's been a busy last couple of days with many deals being done but hopefully this concludes our business for the window and we can now concentrate on winning football matches and climbing the table."