Davies entered the guilty pleas when he appeared at Westminster Magistrates’ Court on Friday.
The first charge was providing false or misleading information for allowances claims contrary to section 10 of the Parliamentary Standards Act 2009.
He admitted that in March 2016 he made a claim under the MPs’ allowances scheme and provided an invoice that he knew to be “false or misleading”.
The second charge was attempting to provide false or misleading information for an allowance claim using an invoice “that he knew to be false or misleading” in April 2016.
Thomas Forster QC, defending, told the court Davies accepts his responsibility and expresses his “sincere and unreserved apology for what he has done”.
Mr Forster said of the 51-year-old: “A disastrous accounting episode, as far as he is concerned.
“He recognises he is the author of his own misfortune, all of this has to be laid at his door and blames no-one else but himself.”
The court heard Davies had already informed Commons Speaker John Bercow of his intention to plead guilty.
Mr Forster said his client, who was seated in the dock wearing a grey suit and pink shirt, is a “family man” with two children who is local to his constituency.
“It took courage to plead guilty and face the music,” Mr Forster added. “He has not shied away from that responsibility and he should be given credit.”
Davies was charged in February this year.
He served as a councillor in Powys before he was elected as MP for Brecon and Radnorshire at the 2015 general election, beating incumbent Liberal Democrat Roger Williams with the seat’s largest majority since 1983.
In January 2018, he was appointed Private Secretary to the Wales Office.
Before entering politics he worked as a rural auctioneer, an estate agent and also managed a mixed veterinary practice in Hay-on-Wye.