The Deputy Prime Minister and Liberal Democrat leader left the door open for a possible return to the front bench for Mr Moore in future, telling him he had "no doubt there will be an opportunity for your talents to be deployed" in government again.
Mr Moore was replaced as Scottish Secretary by fellow Lib Dem Alistair Carmichael, who was the party's chief whip, as the Government began its long-expected reshuffle.
The Lib Dem leader told Mr Moore he was going to be axed on Friday, Mr Clegg's letter revealed.
Mr Clegg said Mr Moore became Scottish Secretary at a "critical time" in the country's relationship with the rest of the UK and "managed the challenges of the situation with great skill and effectiveness".
But he added: "As we discussed when we spoke on Friday, I believe we now need to draw on different experience in the final year running up to the referendum itself and I am keen that, just as we have benefited from your formidable skills over the past three years, that we take advantage of other experience within our ranks during this period.
"I am immensely grateful for all the work you have done at the Scotland Office and for the very significant contribution you have made to the first coalition government in 70 years. I have no doubt that there will be an opportunity for your talents to be deployed in government in the future."
Mr Moore replied: "This has been, and will continue to be, a hugely important time in Scottish politics and that has made it a challenging and rewarding time to be Secretary of State for Scotland."
He added: "In leaving the Scotland Office I am pleased that Alistair will be succeeding me. As a good friend and long-time colleague, I believe he will do a superb job. I wish him all the best."