Cheryl Gillan has promised a "common sense approach" after being appointed Welsh secretary in the new Conservative-Liberal government.
Cardiff-born Mrs Gillan, 58, has served as shadow Welsh secretary since 2005 and will be the first woman in the job.
Former Welsh Secretary, Peter Hain, congratulated the Chesham and Amersham MP but asked why none of the 11 Tory and Lib Dem MPs in Wales were suitable.
Plaid Cymru said an appointment from outside Wales was a "throwback".
Mr Hain said the decision to appoint a Welsh Secretary from an English constituency "will baffle and indeed anger many people in Wales".
"Far from representing the new politics that people want to see, this smacks of the bad old days.
"Between the Conservatives and the Liberal Democrats they have 11 MPs in Wales - are David Cameron and Nick Clegg really saying that none of them are up to the job?
"There is no reason why Mr Cameron's faith in Mrs Gillan could not have been rewarded by offering her another post in a cabinet sadly lacking in women.
"It would have seemed more sensible, and sensitive, to offer the job of Welsh Secretary to a Welsh MP."
Wales Labour First Minister Carwyn Jones also congratulated Ms Gillan.
He said: "I look forward to meeting her at the earliest opportunity to discuss a range of matters relating to Wales and to developing a constructive relationship, to ensure the priorities of the people of Wales are paramount."
Wales Office ministerial appointments are not expected until later.
Mrs Gillan served as a Conservative spokesman on trade and industry, foreign affairs and home affairs before succeeding Bill Wiggin, an opponent of the Welsh assembly, as Shadow Welsh Secretary in December 2005.
She had earlier served as a junior minister in John Major's government.
Mrs Gillan said: "As a politician with proud Welsh roots, it is a great honour to be appointed Secretary of State for Wales.
"And as the first woman to be appointed Welsh Secretary, I look forward to using a common-sense approach to help cut through the bluff and bluster of Welsh politics to deliver the fairest deal and safeguard the best possible services for the people of Wales.
"We have a wonderful country with a rich heritage, diverse culture and an exciting, vibrant future."
Assembly Conservative leader Nick Bourne said said: "I have valued our close working relationship since her appointment to the shadow cabinet in 2005 and look forward to that continuing in the interests of Wales now that Cheryl has taken up her new role.
"I hope Cheryl's appointment will mark the start of a new, positive relationship between the UK and Assembly governments, and between the Assembly and Westminster."
He welcomed the fact she was the first woman - and 15th - Welsh Secretary and called it an "historic achievement" for Mrs Gillan and for the Conservative Party.
Kirsty Williams, leader of the Welsh Liberal Democrats, wished Mrs Gillan well in her job.
"The real test for her now is to show how committed she is to Welsh devolution," said Ms Williams.
"Cheryl Gillan has to stand up for the people of Wales and give us a say on how we want our devolution to proceed. An early referendum on further law making powers for Wales will be her first test."
Plaid Cymru's Commons leader Elfyn Llwyd MP said: "Unfortunately, instating a Secretary of State from outside Wales will be widely viewed as throwback to the 1990s.
He said the request for a referendum from the Welsh Assembly Government on more law making powers was "on top of her desk" and he looked forward to a "prompt call" for it to be held as Mrs Gillan said previously that she would not stand in its way.
Mr Llwyd added: "There will be some people in Wales who will underwhelmed at this appointment but I hope Ms Gillan will make every effort to work with the Welsh Assembly Government - and also to spend time in Wales so that she is able to find out the issues affecting our country."
Mrs Gillan said she would be seeking to meet Carwyn Jones as "soon as possible" to discuss the Welsh economy and a referendum for further legislative powers for Wales.
Meanwhile, the assembly government's deputy first minister said they have "no plan" to deal with an estimated £220m cut to the Welsh budget this year.
The Conservative-Lib Dem coalition at Westminster has announced it will press ahead with billions of pounds of cuts immediately, to start dealing with the UK budget deficit.