The defender is eligible to play for both England and the Republic of Ireland.
"I'm absolutely delighted to have got the contract done, signed and to commit my future to the club until 2024", Rice said.
"I am still young, so to put more years on my contract and keep developing here is the best thing for me to do now", said academy graduate Rice. From the first minute, we had the intention of winning the game and I thought we were very balanced in the whole game.
The Hammers find themselves in the midst of an injury crisis and that may well provide Silva with more opportunities to play in January - and it seems their supporters want to see more of him.
"I see Declan work every day and so it is hard for me to be surprised by him now", Pellegrini said earlier on Friday, before the news of the new deal broke. "We just focus on performances".
"Then the media started about his contract and his money, but he has never had any problem in that sense".
Rice has come through the ranks in east London after joining the club at the age of 14, with club veteran Noble acting as a mentor for his fellow midfield en-route to the 19-year-old becoming a first team star at the London Stadium.
Stu ForsterBurnley's Chris Wood scores under pressure from West Ham's Issa Diop
McCarthy twice saved at his near post as Anderson looked to set the seal on the three points as well as claiming the match ball.
West Ham transfer news: "The plan was to stay with Hammers".
Pellegrini has transformed West Ham's fortunes after the disastrous opening sequence of four straight Premier League defeats, leaving the ex-Manchester City boss pleased with his side's tally at the season's halfway stage.
However, City - now struggling to keep pace with Liverpool at the top of the Premier League - are preparing a January move for the versatile star.
Antonio had some success on the right wing, aided by Diangana, but this was to prove one of those days for the hapless Hammers who remained second best in the second half.
Burnley have won just one of their last 12 Premier League games (D2 L9), conceding 30 and scoring just eight in that run.
The 25-year-old now boasts seven goals in his last nine West Ham games, but Pellegrini still expects him to improve upon that in the second half of the season.
Markets Right Now: US stocks open lower as sellers return
Despite Wednesday's rally, stocks are on track for their worst December since 1931, during the depths of the Great Depression. The S&P 500 was down 20.06 percent from an intraday record high set on September 21 before Wednesday's sharp rebound.