Beblawi, a former undersecretary of the UN's Economic and Social Commission for Western Asia, will oversee economic policy in the new cabinet, which is expected to be unveiled on Monday, the official MENA news agency reported.
Silmi will handle "democratic transition" matters, it added.
Protesters have staged a sit-in for a week in Cairo's Tahrir Square, which was the centre of nation-wide demonstrations that forced president Hosni Mubarak to resign in February.
Subsequent protests persuaded the military, which temporarily assumed power, to sack Mubarak's surviving cabinet in March and appoint a new caretaker government headed by the pro-revolt Sharaf.
The protesters now want a coherent transition to civilian rule and the speedy trials of former regime officials responsible for the killings of anti-regime demonstrators during the revolt.
State media reported that up to 15 ministers will be replaced on Monday.
Sharaf pledged on Friday that "the new ministerial changes are simply the beginning."
"I am working hard to achieve your aspirations," he wrote on his Facebook page.
Sharaf, who has already ordered the sacking of hundreds of senior interior ministry officers, hopes the new cabinet will satisfy the activists while helping the country recover economically.
Egypt has seen a sharp decline in tourism and increased unemployment since the revolt, and investors remain jittery over sporadic and sometimes deadly unrest in the Arab world's most populous country.
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