Rice sealed a move to the Gunners in a club-record £105million deal in the summer, and has had a bright start to life at the Emirates.
The 24-year-old joined the Hammers in 2014 after being released by Chelsea, and instantly became a fan favourite, taking over the captaincy from Noble, following his retirement.
Rice revealed he spoke to Noble along with David Moyes over his move to Arsenal, insisting he did not want to leave on bad terms.
"I called David Moyes and we had a really nice conversation. I felt like we owed it to each other to speak - I have so much respect for him," he told FourFourTwo.
"I talked to Nobes [Mark Noble], too: it was a hard one for him because he's Mr West Ham, but he was buzzing for me.
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"He was so happy that I could push myself and compete in the Champions League this year.
"He said, 'It's nothing more than you deserve'. Some of the players messaged me as well - I had plenty of replies in the group chat we shared together, I was taken aback.
"They're all such close friends of mine and I speak to them regularly. I texted the manager ahead of the first game this season, simply to say, 'Good luck for the season and see you soon'. He replied, which was nice."
Rice has been an instant hit at Arsenal, starting all of their seven Premier League matches so far.
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The England international also netted his first goal for the club, a 96th-minute stoppage time strike against Manchester United in September.
Rice will welcome his former side West Ham to the Emirates on Boxing Day.
"It'll be pretty strange when I play against West Ham this season, because there are so many lads I know and get on with - they'll be saying stuff on the pitch, I'm sure!" Rice added.
"We've got them at the Emirates Stadium first, then at the London Stadium later in the season. It'll be brilliant to go back there and see everyone."