Make his backstory relevant to the plot
What is the role of this NPC in your new campaign? If the answer is something like "given what happened in the previous one, this NPC should logically be present" then it is not enough and you should either remove it from the spotlight or find better reasons as the players won't really care about this previous campaign they didn't even play. We are looking here for narrative reasons like "he will fill the role of the old hermit" or "it will be X's nemesis".
I am not telling you to force the NPC in this role independently of the evolution of the campaign, but just to have an idea of why the NPC will make the campaign better, or you will be way better just not including them.
Now you can think about how to present the backstory as facts that give an advantage to PCs from knowing them. Does it bring keys on how to progress, like the weakness to fire of a foe or the crack addiction of someone they have to bargain with, or the mention of a lost city where they can find some secondary McGuffins ? If it contains such information it is easy to make parts of the backstory told either by the NPC (as an ally, to help them achieve their goals) or by something else (someone wrote a biography about them, or an information dealer spied him because they looked suspicious). As they are looking for useful information the players will pay more attention.
So you search the library for the plans of Castle Doom? You don't find the plans, but there is in one book a chapter about an adventurer who apparently managed to escape its dungeons. He was Imprisoned because...
"Ya see this scar? 'cause of Enpeasea. What (burps), y'on't know the famous Enpeasea? 'Can't 'liev it, she's most terrible bandit 'round here. Robbed even the relic of Santa Robert, Disguy know teh full story and 'll tell ya I ain't lyin'."
No, I know we are working together but I can't let you have my ring, even just for a minute. It was a gift for a dear friend I lost during the Plague. I couldn't heal him but I can respect his vow that I will look after his ring.
Anyway you should probably not throw all the full backstory at once unless at some point the players ask for the full story. Proceed by small bits, it tastes better like that.