Republic of Ireland manager McCarthy said: "Declan rang me today and said he has made a decision to give it a go with England".
"Sad to hear, but good luck with England", one wrote.
Between 2015 and 2018, he represented the Republic of Ireland at under-16, under-17, under-19 and under-21 levels, playing 20 times in total.
"I have also spoken to Martin O'Neill, Mick McCarthy, Gareth Southgate and to friends and colleagues within the game whose opinion I respect". "Particularly not for a young lad who never dreamed of being in this position".
With Irish heritage but born in London, Rice says he considers himself "to be of mixed nationality".
"Ultimately it is a personal decision that I have made with my heart and my head, based on what I believe is best for my future".
"My pride at wearing the Irish shirt was always 100 percent genuine", he added.
Rice broke the news on his Twitter account via a lengthy statement and took the opportunity to thank Mick McCarthy and the FAI for their "support" and "understanding" of his decision to represent England. It was a great honour for myself and my family, and something I will always cherish.
"I would also like to make it clear that, in requesting to transfer my national team representation, I am not taking for granted a call-up to the England squad or making any assumptions about my future worldwide career".
In a statement posted on Twitter, Rice confirmed his intent to file a one-time switch with Federation Internationale de Football Association and change his worldwide allegiance to England.
Rice has made 23 Premier League appearances for West Ham this season, scoring one goal.