The outspoken Archbishop also appealed to people to shun the farcist British National Party at the General Election and called for an England victory at the World Cup.
Writing in a national newspaper, Dr John Sentamu also said he would be praying for the safe return of both Claudia Lawrence and Madeleine McCann in 2010, and spoke about the continued fighting in Afghanistan and the situation in Zimbabwe.
But he led with a call for people to dump the BNP.
The archbishop said: “I hope there will not be a repeat of the fatigue, distrust and disinterest that allowed the BNP to gain two seats in the European Parliament last year.
“Where I live, in Yorkshire, the BNP vote decreased by over 6,000, but their representation increased because a large majority of people did not come out and vote for mainstream political parties.
“I hope we will not make the same mistake at the General Election and allow candidates with sectarian, divisive and engineered hatred into Parliament via the back door."
He said there was a moral responsibility for everyone to vote.
He quoted historian Edmund Burke: “All that is necessary for the triumph of evil is that good men do nothing."
He said he hoped 2010 would see a regime change in Zimbabwe, and the removal of Robert Mugabe.
Together we can make 2010 a year to remember.
“A year in which all of us exercise that greatest gift – of charity.”