Mr. Brownback will leave Kansas at a time of uncertainty over funding for public education. The Kansas Supreme Court is expected to rule soon on the constitutionality of the state’s new school funding mechanism.

“He leaves behind a legacy of failed leadership,” said State Representative Melissa Rooker, a moderate Republican who has frequently opposed Mr. Brownback’s policies. She said she did not know what to expect from Mr. Colyer, a Republican and an ally of Mr. Brownback’s, because he was not involved in the day-to-day dealings of the Legislature.

Representative Jim Ward, the Democratic leader in the Kansas House, said he was “not surprised” to hear of the appointment, which has been rumored in Topeka for months.

“I’m not going to miss him,” Mr. Ward said. “He has left a state in carnage and destruction.”

Mr. Ward said that he believed the governor “had the background” for his new role, but that “he hasn’t embraced diversity” consistently in Kansas. “Hopefully, this job that he’ll step into, he’ll realize that Americans are of all kinds of faith,” Mr. Ward said.

Representative Ron Ryckman Jr., a Republican and the House speaker, said Mr. Brownback was “uniquely qualified” for the ambassadorship. “I wish him all the best in his new post and would like to express my gratitude for his extensive service to the State of Kansas,” he said.

Kris Kobach, the Republican secretary of state, who is running to succeed Mr. Brownback, said, “He is the first truly conservative governor that Kansas has had in the last 40 years, and so he definitely made history in that respect.”

Mr. Kobach added, “On the other hand, though, he faced a real battle at the end to preserve the tax cuts, and I wish he had won.”