The pair join Feyenoord left-back Tyrell Malacia as the Dutchman’s three key signings so far as he looks to inject new life into the Old Trafford team after their woeful campaign last season.
United, who last won major silverware in 2017, finished sixth in the Premier League with their lowest points total since the league was launched in 1992.
Danish midfielder Eriksen was signed as a free agent on Friday after leaving Brentford with Argentine defender Martinez joining the club from Ajax two days later.
Ten Hag said the experience of Eriksen, 30, would be vital and his creativity a boon for the front line, potentially spearheaded by Cristiano Ronaldo, although the superstar striker’s future with United remains unclear.
“I think he (Eriksen) is a magnificent football player and I think the fans will enjoy watching him, because he’s creative, he has ideas,” the manager said on the club website from Melbourne, where they are on a pre-season tour.
“I think especially our strikers will also be happy because he’s the one who can involve them in the game.
“He’s an experienced player. He plays in countries abroad, in Italy, in Holland, a long time in England, so he knows the Premier League. It’s an absolute advantage that we have him in.”
Former Tottenham star Eriksen’s switch to the Red Devils completes an incredible return after his brush with death last year.
Eriksen suffered a cardiac arrest on the pitch in Copenhagen while playing for Denmark at the European Championship and was forced to leave Inter Milan after recovering due to Serie A health regulations.
Fitted with an implantable cardioverter defibrillator, he proved his form and fitness during a loan spell at Brentford in the second half of last season.
– ‘Fighting spirit’ –
Martinez, 24, joined from Ten Hag’s old club Ajax, subject to a medical, player terms and UK visa requirements, with the manager saying he couldn’t be happier.
Ajax confirmed United will pay an initial 57 million euros ($57 million, £48 million) with a further 10 million euros in performance-related bonuses.
“He’s a warrior and I think the fans will admire him. He has an attitude, fighting spirit,” he said.
“He brings aggressiveness to the game, in a good way. I think we need that. But also, he’s skilful and he can deal with the ball and he’s left-footed.”
Ten Hag said he believed Martinez had the right character to adjust to Premier League football and was familiar with his methods given their time together at Ajax.
“I think the Premier League is high intensity, lots of challenges. We need such players (with fighting spirit),” he said. “Certain ideas, he knows them. That is an advantage, clearly.”
While Malacia is on the pre-season tour to Thailand and Australia, which has seen United beat Liverpool 4-0 in Bangkok and Melbourne Victory 4-1, Ten Hag confirmed neither Martinez nor Eriksen would join the squad for their final two games in Australia against Crystal Palace and Aston Villa.
“Unfortunately we cannot have them here on the tour, because at the moment they arrive here we will fly back,” he said.
“We cannot wait to involve them in our squad and the fans also cannot wait.”