HARARE, Zimbabwe — Zimbabwe’s President Robert Mugabe, who once vowed to rule for life, resigned on Tuesday, succumbing to a week of overwhelming pressure from the military that put him under house arrest, lawmakers from the ruling party and opposition who started impeachment proceedings and a population that surged into the streets to say 37 years in power was enough. The capital, Harare, erupted in jubilation after news spread that the 93-year-old leader’s resignation letter had been read out by the speaker of parliament, whose members had gathered to impeach Mugabe after he ignored escalating calls to quit since a military takeover.