SALEM, Ore. — Boris Berian, until last week the target of a Nike lawsuit that stemmed from a contract disagreement, on Thursday announced he was signing with New Balance, a rival shoe company and sponsor of his track club. The move was not entirely unexpected. Berian had expressed his desire to sign with New Balance, had promoted its products on his social media accounts and stated in court filings that he preferred competing in their shoes. “I appreciate the values that New Balance represents, and it is clear to me that New Balance cares about runners,” Berian said in a statement. The announcement comes a week after Nike dropped a lawsuit it had filed at the end of April contending that Berian, a 2011 graduate of Widefield High School near Colorado Springs and the favorite in the 800 meters at the U.S.