CROWN Prince Frederik, Denmark's future king, yesterday became officially engaged to an Australian law graduate of Scottish descent.

The 35-year-old prince will marry Mary Donaldson, a 31-year-old from Tasmania, Australia, next May 14 in Copenhagen, the Danish capital.

Miss Donaldson is the first Australian-born woman to stand in line to become a European queen.

Queen Margrethe, the prince's mother, officially approved the engagement at a meeting with the Danish government yesterday, the palace said in a statement.

''Her majesty and his royal highness Prince (Henrik) have the joy to announce that his royal highness, the Crown Prince has been engaged to Miss Mary Elizabeth Donaldson,'' the palace said.

The couple appeared four times on the balcony of the royal palace to greet about 20,000 people waving Danish and Australian flags in the palace square. They ignored calls from the crowd to kiss each other.

The formal engagement had been expected since the marriage was first announced last month.

Miss Donaldson, of Hobart, Tasmania, will convert to the Danish Lutheran Church from the Presbyterian Church and replace her Australian and British citizenships with a Danish passport, the palace said.

The wedding will be performed by Copenhagen Bishop Svend Norman Svendsen and Christian Thodberg, royal chaplain. It will take place at Our Lady's Church, Copenhagen's Lutheran cathedral.

John Dalgleish and Henrietta Clark Donaldson, Miss Donaldson's parents, emigrated from Scotland to Australia in 1963 and became Australian citizens in 1975.

Her mother died in 1997 and her father, a professor of mathematics who is currently lecturing at Oxford University, remarried in 2001 to Susan Moody, a British novelist. Miss Donaldson has two sisters and a brother.

Under the constitution, Denmark's popular 63-year-old monarch and the government must give their formal approval for Prince Frederik to marry.

Last month, Anders Fogh Rasmussen, the Danish prime minister, said his government supported the engagement.