Cabinet Office minister Michael Gove said the new investment would ensure businesses trading internationally could “manage the changes and seize the opportunities” arising from Brexit.
The £705 million will be split between £470 million for port and inland infrastructure and £235 million for new staff and IT systems.
Of the £235 million, £100 million will be spent on customs to help businesses trade more easily, £20 million will go on security equipment, £15 million will be used for data tools to help manage the border and £10 million will be spent on recruiting 500 more Border Force staff.
This funding is only for the border between Great Britain and the EU. Spending on the Northern Ireland-EU border will be announced later, the Government said.
Mr Gove said: “We are taking back control of our borders, and leaving the single market and the customs union at the end of this year bringing both changes and significant opportunities for which we all need to prepare.
“That is why we are announcing this major package of investment today.
“With or without further agreement with the EU, this £705 million will ensure that the necessary infrastructure, tech and border personnel are in place so that our traders and the border industry are able to manage the changes and seize the opportunities as we lay the foundations for the world’s most effective and secure border.”
The news comes after reports emerged that the Government had bought a large plot of land in Kent as a customs clearance centre for the 10,000 lorries that come through Dover from Calais every day.
Work will soon begin on the 1.2 million hectare site near Ashford, 20 miles from Dover.
The UK will finish its transition period at the end of 2020, leaving the customs union and single market.
The new spending announcement comes ahead of guidance being given to traders and hauliers explaining what they may need to do to prepare for the end of the year.
Meanwhile, the Sunday Telegraph reported that Chancellor Rishi Sunak could bring in tax cuts and overhaul planning laws in up to ten new freeports – where UK taxes and tariffs would not apply.
Mr Sunak is reported to be planning to open bidding for towns, cities and regions to become freeports in his autumn Budget.
The ports will be “fully operational” within 18 months of the UK leaving the customs union and single market at the end of this year, the paper reported.