The top-10 duo made history for their nation earlier this year when they squared off in an unprecedented all-Czech final at Wimbledon and have now added to their growing list of achievements by clinching the Czech Republic's 12th BJK Cup trophy.
Noskova sealed the 2-0 victory with a 6-3, 7-6(5) win over world number seven Elina Svitolina after Muchova had put the Czechs in front with a 6-2, 6-3 rout of Anhelina Kalinina.
Czech captain Barbora Strycova is a six-time champion and was a player on the team that beat the USA in the final in 2018.
She has become just the fourth woman to win the BJK Cup as both a player and a captain - joining Margaret Court, Chris Evert and King herself.
Ukraine were competing in their first-ever BJK Cup final after they knocked out two-time defending champions Italy in the previous round.