Ase, 29 is a stand-off and Watson, who is six years younger, plays at half-back.
The brothers both represented the Kumuls in the 2017 World Cup and were members of the PNG Hunters team which won the Intrust Super Cup last season.
Ase, who also featured in the 2013 World Cup, captained the Hunters to the minor premiership and Grand Final, when he was man of the match.
Both were part of PNG’s gold medal-winning rugby league nines team at the 2015 Pacific Games.
Rovers general manager Davide Longo said: “We are very excited to announce the signings of the Boas brothers.
“They are two hugely talented players who have experience of winning and playing at an elite level.”
Gareth Hock and Tom Holmes have left Rovers since they missed out on a place in the Betfred Qualifiers, but Longo insisted: “This is only the start of our recruitment for the 2019 season and there will be more reasons for supporters to be excited.”
The brothers are due to arrive at Featherstone in January. The signings come after Rovers fielded only 14 players in their 22-4 Championship Shield win over Leigh Centurions.
Coach John Duffy had named 15 in his initial squad, but Dakota Whylie failed a head test. That result took Rovers two points clear at the top of the table and could secure home advantage in the final against Leigh.
Duffy said: “It was a top performance from us, it was real backs-against-the-wall stuff.
“The players are a very special group and they have turned up for each other again against a very good Leigh side.”