To answer my own question, numbers shown in bold below are the FIDE ranking of the player at the time they were crowned World Champion. Before 1964 there was no ranking system as far as I know. Ranking taken from FIDE rankings site and this chess USA education webpage.
Undisputed world champions 1886–1993
?? Wilhelm Steinitz (1886–1894)
?? Emanuel Lasker (1894–1921)
?? José Raúl Capablanca (1921–1927)
?? Alexander Alekhine (1927–1935, 1937–1946)
?? Max Euwe (1935–1937)
?? Mikhail Botvinnik (1948–1957, 1958–1960, 1961–1963)
?? Vasily Smyslov (1957–1958)
?? Mikhail Tal (1960–1961)
01 Tigran Petrosian (1963–1969) (first unofficial rankings list 1964)
02 Boris Spassky (1969–1972)
01 Bobby Fischer (1972–1975)
02 Anatoly Karpov (1975–1985)
02 Garry Kasparov (1985–1993)
Classical (PCA/Braingames) world champions 1993–2006
01 Garry Kasparov (1993–2000)
03 Vladimir Kramnik (2000–2006)
FIDE world champions 1993–2006
02 Anatoly Karpov (1993–1999)
44 Alexander Khalifman (1999–2000)
02 Viswanathan Anand (2000–2002)
07 Ruslan Ponomariov (2002–2004)
54 Rustam Kasimdzhanov (2004–2005)
03 Veselin Topalov (2005–2006)
Undisputed world champions 2006–present
09 Vladimir Kramnik (2006–2007)
01 Viswanathan Anand (2007–present)
Next undisputed world champion ?
04 Viswanathan Anand
20 Boris Gelfand
And as I write this Anand has won game 8.
Also, an interesting quote from Alexander Khalifman responding to his very low ranking at the time of his crowning FIDE world champion in 1999:
"Rating systems work perfectly for players who play only in round robin closed events. I think most of them are overrated. Organizers invite the same people over and over because they have the same rating and their rating stays high."
Of course he would say that but perhaps some truth there.