Per this interview, it's a mix of Czechoslovakian and the parole officer (Mr Deltoid) from the film 'A Clockwork Orange'. It's supposed to convey a sort of "courtly" tone.
Jurasik: The quick story about the accent, if I can tell you how I patchworked it together, is I was doing a play downtown, a Tennessee
Williams play, and I worked really hard on a Memphis accent. I felt
like I had really nailed it. But one L.A. critic nailed me and said,
"That’s a terrible Memphis accent. That doesn’t sound like a Southern
accent." I was really hurt. About that time was when "The Gathering,"
the pilot, showed up. I called Joe and said, "What do you want me to
sound like?" He said, "Let him sound like whatever you want," so I
purposely took a couple of different things. There’s a character who
plays the parole officer in A Clockwork Orange, the guy who’s always
saying, "And night-time is the best time, um, yes?" I took my
Czechoslovakian grandmother. I had spent three consecutive summers in
Ireland. I didn’t always take sounds; I took rhythms. Londo had a kind
of musical thing.
Peter Jurasik (Dr. Geiger) Chat at I.D.I.C Online on July 10, 1999
Apparently there's also a little bit of an irish brogue in there as well. Note that he's told the story so many times that the quote below is almost identical, despite being nearly two years apart.
Jurasik: The story I always tell in conventions, which is true, is I had just finished a play in Los Angeles, a Tennessee Williams play, and I had gotten bad reviews for a Memphis accent that I did. And I had worked really hard on this Memphis accent, and I had it nailed perfectly and people from Memphis said to me, "Wow, you sound like you grew up next door to me." Then some dumb ass reviewer said, "That's not a very good Memphis accent."
IGNFF: From L.A.
Jurasik: Yeah, from L.A. He wouldn't know a Memphis accent anyway. But
being the insecure actor that I am, I took that hard. You take stuff
like that, when it's in the L.A. Times, it hurts you anyway ... When I
got Babylon, I realized this is a great opportunity for me. I will be
the first Centauri, and I can make him talk anyway he wants, and no
reviewer will ever be able to say, "That's not what a Centauri sounds
like. What a terrible Centauri accent he's doing." Because I'm the
first Centauri, so I make him talk any way I want. So, I made the
accent up, a kind of amalgam of a number of different accents. I used
a little of my Slovak grandmother, and I mentioned Ireland; I love the
rhythms of Irish. So I mixed it up and made it my own.
AN INTERVIEW WITH PETER JURASIK
In-universe, showrunner JMS described it as being associated with the upper classes, hence why younger (and lower class) Centauri like Vir have a different accent but that Refa and Emperor Turhan sound similar.
Q. Speaking of Londo's accent, I'm assuming that different Centauri
accents represent people from different areas of the planet?
Anything significant in all this, or just a bit of
JMS: No, we've just always assumed that not everyone on any given
planet is going to speak with the same accent as everybody else from
that planet. Seems more realistic.
Certainly, among Centauri, a certain accent is more associated with
the "old school" of court nobility and the like.
JMS: Aol Chat