Shares rose 2.02% to 630p in afternoon trading.
The defence company had faced a big hit to its sales if the case against the Secretary of State for International Trade was successful, since Saudi Arabia is one of its largest customers.
The Campaign Against Arms Trade (CAAT) had brought the case, claiming that permission for arms sales to Saudi Arabia should be refused as policy states that licences must be denied if there is a “clear risk” that arms could be used in “a serious violation of International Humanitarian Law”.
CAAT said Saudi Arabia’s military action in Yemen, in which 10,000 people have been killed during a bombing campaign led by the Middle Eastern nation, constituted a violation of this law.
Saudi Arabia has insisted that it is not targeting civilians in leading an international coalition against Houthi rebels who pose a major threat in the neighbouring country.
High Court rules there is no risk to violations of humanitarian law in Saudi Arabia
The case was thrown out of the High Court by Lord Justice Burnett and Justice Haddon-Cave, who concluded that the Secretary of State was “rationally entitled to conclude” the coalition was not deliberately targeting civilians.
The judges ruled that Saudi Arabia was respecting humanitarian law and is in “constructive dialogue with the UK about its processes and incidents of concern”. They added there was no “real risk” that there might be serious violations of International Humanitarian Law.
The decision was made after the judges reviewed publicly available information and secret material supplied by the Ministry of Defence.
Saudi Arabia accounted for about 21% of BAE’s £19bn annual sales last year.
CAAT to appeal High Court decision on arms exports to Saudi Arabia
A spokesman for CAAT said: “This is a very disappointing verdict, and we are pursuing an appeal. If this verdict is upheld then it will be seen as a green light for government to continue arming and supporting brutal dictatorships and human rights abusers like Saudi Arabia that have shown a blatant disregard for international humanitarian law."
"This case has seen an increased scrutiny of the government’s toxic relationship with Saudi Arabia. It is a relationship that more than ever needs to be examined and exposed."
BAE was unable to be reached for comment.