Or you can also put "καλύτεροι φίλοι", but if I were you, I wouldn't.
Example: "John and Mike are best friends = Ο John και ο Mike είναι καλοί φίλοι.

If the context is informal, I think that "kolliti" is the best choice: the other answers are also correct, but "kolliti" is more what people -especially young people- call eachother. any other choice may seem awkward, too typical.

Είμαστε κολλητοί Imaste kollitI= we are best friends

Otherwise, o kollitOs mou (masc)/ i kollitI mou (fem)= my best buddy
ο κολλητός μου/ η κολλητή μου

If it's not so informal, or about older people, "kali fili" would also be appropriate.

the expression "kaliteri fili" is used only when talking about the people themselves, and not the relationship. That is,

he's my best friend = Ιne o kalΙterΟs mou fΙlos είναι ο καλύτερός μου φίλος

she's my best friend = Ιne i kalΙterΙ mou fΙli είναι η καλύτερή μου φίλη

we're best friends = Ιmaste kalΙ fΙli.
Είμαστε καλοί φίλοι

It all depends on the degree and the type of friendship.It is also a matter of how sentimental and into the friendship the speaker is. specifically for "best friends" I would suggest "poli kali fili", which means " we are the closest it can be".