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By C. Bryson Hull and Wangui Kanina

NAIROBI, March 18 (Reuters) - Kenya's parliament on Tuesday unanimously approved a power-sharing deal designed to end the post-election crisis that killed at least 1,000 people in the east African country.

Legislators passed the legal changes needed for a coalition government in which President Mwai Kibaki can bring in rival Raila Odinga as prime minister following their agreement last month.

Investors in Kenya's economy -- knocked hard by the crisis but still seen as being among Africa's most promising -- are keenly watching whether the deal will go through smoothly.

Violence erupted after Odinga accused Kibaki of stealing the December election. In addition to the killings, at least 300,000 people were left homeless.

Odinga's party and Kibaki's coalition will each name a deputy prime minister. The cabinet will also be split evenly between both sides to form a unity government. It was not immediately clear when that would happen.

The new administration must then tackle the bigger task of changing Kenya's constitution within 12 months to address underlying issues of power, inequality and land which the eruption of political violence laid bare.

"Where we have come to now is a joy," Kibaki told parliament before Tuesday's vote, making a rare appearance in his capacity as a legislator.

"We are genuinely seeking a solution to our problem. I am quite sure myself that we have found an answer."

Odinga also addressed the chamber before the vote:

"We know why we are where we are, but let us get out of this place. We need to feel part and parcel of one and the same. Let us now fuse together as one people who want to do something for the people of Kenya," he said to loud applause.

Matters of land, power and inequality had cropped up during violence in earlier elections, but never on the scale they did this time around -- dealing a big setback to an economy powered by tourism, trade and agriculture.

Parliament has come under widespread criticism from Kenyans in the past.

Legislators have often failed to make the quorum needed for decisions to be taken despite working two days in each week and only 26 weeks a year. With salaries on par with U.S. senators and home loans plus generous car allowances, members of parliament are in the ranks of Kenya's rich elite. (Editing by Matthew Tostevin)

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