Fulham have the option to recall Johnson in January if they require.
Johnson is City's second signing this week following the arrival of Hungarian defender Gabor Gyepes.
Johnson has had limited chances with Fulham but boasts a reasonable scoring record in the MLS. He has also scored a dozen goals for the USA National side.
"Hopefully we've picked up another good player that will come in and help the cause," Cardiff boss Dave Jones said.