The pair were the centre of attention throughout last season as both drivers ignored team orders over the season, with this coming to a head when the pair made contact with each other and both retired during the Brazilian Grand Prix.
Button believes, however, that things will be better for the duo in 2020 and that they can work together as a team to challenge Mercedes for the title.
"They had a few incidents in 2019, hopefully, this year that won't be the case. They are both very quick," Button told Sky Sports.
"I think last year they were both trying to find their position in the team. The new guy coming in, Charles Leclerc, and getting more pole positions than anyone, and Sebastian Vettel, the four-time world champion.
"Two very talented drivers and I think after that first year together now they can really work as a team and focus on fighting Mercedes, not just fighting each other."
Button also stated that he thinks both Sebastian Vettel and Charles Leclerc are one of the strongest pairings in F1, despite their attempts to better each other throughout 2019.
Leclerc, in his debut season with the Ferrari team, managed two victories and more pole positions than any other drivers in 2019 with seven, while Vettel only managed one win and two pole positions over the whole season.
"I think Sebastian now understands how quick his team-mate is and I think they'll have a much better relationship this year," Button commented.
"They obviously want to beat each other but I do think that pairing is very strong."