He had quite a few.
First Doctor:Susan (Time Lord)
Fourth Doctor: K9 Mark I and K9 Mark II (robot Dogs), Romana (Time Lord), Adric (Alzarian), and Nyssa (Trakenite). Leela was human & her ancestors were originally from Earth but she was born on another planet (whose name was never revealed), long after her people had forgotten their origins.
Fifth Doctor: Adric (Alzarian), Nyssa (Trakenite), Turlough (Trion), Kamelion (Android).
Ninth/Tenth Doctor: Jack Harkness is said to be from the Boeshane Peninsula on an unidentified planet which is not necessarily earth. We also don't know for certain that he is fully human. The one-off companion Astrid Peth (who is listed as a companion by the BBC) was from the planet Sto.
Eleventh: On an ongoing basis, River Song as she was conceived in the TARDIS, born on Demons Run and raised somewhere other than earth (plus there's the "human + Time Lord" DNA). There's also the Gallifrey built/grown TARDIS who was confirmed as a sentient companion in the Doctor's Wife, confirming implications dating back to "The Edge of Destruction" in 1964. Further one-off companions Kazran Sardick and Abigail Pettigrew in a Christmas Carol (who fulfil the companion critiera of travelling with the Doctor on adventures in the TARDIS) seem to be human, but live on an unidentified planet. And then there is also the case of the Silurian Vastra and Sontaran Strax, who "A Good Man Goes to War" established have prior relationships with the Doctor and who qualify at least for one-off companion status (not counting announced future appearances).