"I know that you are committed to help America's economy grow in ways that are good for all its people.
"In the years ahead there will be issues on which we agree, and issues on which we do not. But as you prepare to take office as our new president, I hope the ideas I have offered in this letter represent ways that we can work together to achieve prosperity that is broadly shared in our society."
Last week, Ms Wood slammed the letter, saying she could "no longer contribute to an organisation that would ignore the real needs of its workforce".
"Your letter offered the backing of IBM's global workforce in support of his agenda that preys on marginalised people and threatens my wellbeing as a woman, a Latina and a concerned citizen," she wrote.
"The company's hurry to do this was a tacit endorsement of his position, and has signalled to me something very important about IBM's values: a willingness to legitimise threats to our country for financial gain.
"The President-elect has demonstrated contempt for immigrants, veterans, people with disabilities, Black, Latinx, Jewish, Muslim and LGBTQ communities. These groups comprise a growing portion of the company you lead, Ms Rometty. They work every day for IBM's success and have been silenced by your words."
Ms Wood said IBM should have taken the lead of Pepsico CEO Indra Nooyi, a Hillary Clinton supporter, whose remarks critical of Mr Trump sparked calls for a boycott of Pepsi. It comes after the boss of food delivery service GrubHub sparked uproar by suggesting employees who supported Mr Trump should resign.
"A look at IBM recruitment collateral suggests that the future of the company hinges on realising an inclusive and welcoming culture, though you do not communicate this vision within the many pages of your letter to a man who will soon be in the top office of the United States government," Ms Wood wrote.
"There have been days of protest across the country. Students everywhere - future IBMers - are marching out of their high schools and colleges to express their outrage. The spike in hate crimes that has erupted across this country since the election emphasises what a disservice to your workforce it is to ignore their safety."
She also asked "what will IBM do" if the President-elect "follows through on his repeated threats to create a public database of Muslims". Mr Trump's chief of staff, Reince Priebus, has ruled out any such database.
"The choice to leave IBM did not come lightly," Ms Wood wrote. "I am not leaving for another offer, nor do I have a safety net to fall back on. What I do have is the knowledge that my own life - and those of the several hundred thousand who serve your company worldwide - are too valuable to waste at an organisation where we are not respected."